poincare bendixson theory for leaves of codimension one the level of a local minimal set of a c2 codimension one foliation of a compact manifold is a nonnegative integer defined inductively level zero corresponding to the minimal sets in the usual sense each leaf of a local minimal set at level k is at level k the authors develop a theory of local minimal sets level and how leaves at level k asymptotically approach leaves at lower level this last generalizes the classical poincare bendixson theorem and provides information relating growth topological type and level e g if l is a totally proper leaf at level k then l has exactly polynomial growth of degree k and topological type k

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

on the minimum ropelength of knots and links the ropelength of a knot is the quotient of its length by its thickness the radius of the largest embedded normal tube around the knot we prove existence and regularity for ropelength minimizers in any knot or link type these are c 1 1 curves but need not be smoother we improve the lower bound for the ropelength of a nontrivial knot and establish new ropelength bounds for small knots and links including some which are sharp

knot floer homology detects fibred knots ozsvath and szabo conjectured that knot floer homology detects fibred knots in s 3 we will prove this conjecture for null homologous knots in arbitrary closed 3 manifolds namely if k is a knot in a closed 3 manifold y y k is irreducible and hat hfk y k is monic then k is fibred the proof relies on previous works due to gabai ozsvath szabo ghiggini and the author a corollary is that if a knot in s 3 admits a lens space surgery then the knot is fibred

torsion homology growth and cycle complexity of arithmetic manifolds let m be an arithmetic hyperbolic 3 manifold such as a bianchi manifold we conjecture that there is a basis for the second homology of m where each basis element is represented by a surface of low genus and give evidence for this we explain the relationship between this conjecture and the study of torsion homology growth

linearized cauchy data inversion method for two dimensional buried target imaging we propose a novel inversion algorithm to image buried objects in inhomogeneous media from the electromagnetic data on the outer boundary our method is based on exploiting the cauchy data to derive a new born like linearization of the inverse problem the main advantage of this formulation is to avoid the use of the background green function and therefore is computationally more efficient it also provides better accuracy than classical born approximation in the case of stratified media our approach can be coupled with any appropriate continuation method we discuss here the coupling with a continuation method based on the use of approximate transmission conditions the feasibility and robustness of our methodology is validated through numerical experiments for single and multiple targets

annuli in generalized heegaard splittings and degeneration of tunnel number abstract we analyze how a family of essential annuli in a compact 3 manifold will induce from a strongly irreducible generalized heegaard splitting of the ambient manifold generalized heegaard splittings of the complementary components there are specific applications to the subadditivity of tunnel number of knots improving somewhat bounds of kowng kw for example in the absence of 2 bridge summands the tunnel number of the sum of n knots is no less than frac 2 5 the sum of the tunnel numbers

monopoles and lens space surgeries monopole floer homology is used to prove that real projective three space cannot be obtained from dehn surgery on a nontrivial knot in the three sphere to obtain this result we use a surgery long exact sequence for monopole floer homology together with a nonvanishing theorem which shows that monopole floer homology detects the unknot in addition we apply these techniques to give information about knots which admit lens space surgeries and to exhibit families of three manifolds which do not admit taut foliations

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

multidimensional born velocity inversion single wideband point source the inverse scattering problem for an acoustic medium is considered within the approximate direct inversion framework as opposed to iterative methods the direct inversion approach gives an estimate of the medium velocities by operating on the observed scattered field without repeated solutions of the forward problem previous solutions to the multidimensional born velocity inversion problem require either coincident source and receiver arrays or plane wave sources in both cases an array of point sources is required to collect the proper data for inversion in this paper the solution to the single point source problem is derived it is shown that by extrapolating and imaging the observed scattered field appropriately the projections of the velocity function at all angles can be obtained the velocities are then reconstructed by the inverse radon transform method of tomography

free abelian covers short loops stable length and systolic inequalities we explore the geometry of the abel jacobi map f from a closed orientable riemannian manifold x to its jacobi torus h 1 x mathbb r h 1 x mathbb z mathbb r applying m gromov s filling inequality to the typical fiber of f we prove an interpolating inequality for two flavors of shortest length invariants of loops the procedure works provided the lift of the fiber is non trivial in the homology of the maximal free abelian cover overline x classified by f we show that the finite dimensionality of the rational homology of overline x is a sufficient condition for the homological non triviality of the fiber when applied to nilmanifolds our fiberwise inequality typically gives stronger information than the filling inequality for x itself in dimension 3 we present a sufficient non vanishing condition in terms of massey products this condition holds for certain manifolds that do not fiber over their jacobi torus such as 0 framed surgeries on suitable links our systolic inequality applies to surface bundles over the circle provided the algebraic monodromy has 1 dimensional coinvariants even though the massey product invariant vanishes for some of these bundles

singular surfaces mod 2 homology and hyperbolic volume i if m is a simple closed orientable 3 manifold such that 1 m contains a genus g surface group and if h 1 m 2 has rank at least 4g 1 we show that m contains an embedded closed incompressible surface of genus at most g as an application we show that if m is a closed orientable hyperbolic 3 manifold of volume at most 3 08 then the rank of h 1 m 2 is at most 6

unlinking via simultaneous crossing changes given two distinct crossings of a knot or link projection we consider the question under what conditions can we obtain the unlink by changing both crossings simultaneously more generally for which simultaneous twistings at the crossings is the genus reduced though several examples show that the answer must be complicated they also suggest the correct necessary conditions on the twisting numbers let l be an oriented link in s3with a generic projection onto the plane r let a be a short arc in r2 transverse to both strands of l at a crossing so that the strands pass through a in opposite directions then the inverse image of a contains a disk punctured twice with opposite orientation by l define a crossing disk d for a link l in s3 to be a disk which intersects l in precisely two points of opposite orientation it is easy to see that any crossing disk arises in the manner described twisting the link q times as it passes through d is equivalent to doing llq surgery on dd in s3 and adds 29 crossings to this projection of l we say that this new link l q is obtained by adding q twists at d call dd a crossing circle for l a crossing disk d and its boundary do are essential if dd bounds no disk disjoint from l this is equivalent to the requirement that l cannot be isotoped off d in s3 od here we examine how a link can be turned into the unlink via simultaneous twists on disjoint crossing disks in particular we prove an analogue for pairs of crossing disks of the following theorem a much more general version of which is proven in st 1 41 see also gal

inverse scattering inverse source theory the inverse scattering inverse source problem associated with the inhomogeneous helmholtz wave equation the special case sturm liouville acoustic wave equation and the time independent schrodinger equation is treated to this end the concepts of a reference wave velocity and an associated free reference space green s function spectrum are introduced a modified kirchhoff surface integral containing only the gradient of the real part of this free reference space green s function spectrum and the fields on a measurement surface is formulated yielding an integral equation for the unknown fields and sources in the interior of the closed piecewise smooth surface on which the remotely sensed fields are known a well posed analytic closed form solution of this integral equation for the unknown fields and their laplacians is obtained with the aid of a modified spatial fourier transform in which the reference velocity is continually varied in such a fashion that the ewald sphere shell sweeps to fill

exact output control for a family of linear plants with parameter uncertainties a family of linear continuous time plants parametrized by a vector of unknown parameters taking values in a known finite set is considered the problem investigated consists in finding a linear discrete time compensator that independently of the actual value of the parameter vector guarantees zero continuous time steady state output error with respect to a given continuous time external reference it is shown that the problem admits a solution in the class of periodic controllers

a recursive algorithm for multifrequency acoustic inverse source problems an iterative recursive algorithm is studied for recovering unknown sources of acoustic field with multifrequency measurement data under additional regularity assumptions on source functions the first convergence result toward multifrequency inverse source problems is obtained by assuming the background medium is homogeneous and the measurement data is noise free error estimates are also provided when the observation data is contaminated by noise numerical examples verify the reliability and efficiency of our proposed algorithm

foliations with good geometry the goal of this article is to show that there is a large class of closed hyperbolic 3 manifolds admitting codimension one foliations with good large scale geometric properties we obtain results in two directions first there is an internal result a possibly singular foliation in a manifold is quasi isometric if when lifted to the universal cover distance along leaves is efficienit up to a bounded multiplicative distortion in measuring distance in the universal cover this means that leaves reflect very well the geometry in the large of the universal cover and are geometrically tight this is the best geometric behavior we previously proved that nonsingular codimension one foliations in closed hyperbolic 3 manifolds can never be quasi isometric in this article we produce a large class of singular quasi isometric codimension one foliations in closed hyperbolic 3 manifolds the foliations are stable and unstable foliations of pseudo anosov flows our second result is an external result relating nonsingular foliations in hyperbolic 3 manifolds with their limit sets in the universal cover that is showing that leaves in the universal cover have good asymptotic behavior let g be a reebless finite depth foliation in a closed hyperbolic 3 manifold then g is not quasi isometric but suppose that g is transverse to a quasigeodesic pseudo anosov flow with quasi isometric stable and unstable foliations which are given by the internal result we then show that the lifts of leaves of g to the universal cover extend continuously to the sphere at infinity and we also produce infinitely many examples satisfying the hypothesis the main tools used to prove these results are first a link between geometric properties of stable unstable foliations of pseudo anosov flows and the topology of these foliations in the tuniversal cover and second a topological theory of the joint structure of the pseudo anosov foliations in the universal cover reebless codimension one foliations are extremely useful for understanding the topology of 3 manifolds for instance they imply that the manifold is irreducible ro its universal cover is homeomorphic to r3 pa leaves are 7rl injective no and transversals are never null homotopic no hence they reflect topological properties of the manifold as for which manifolds have reebless foliations gabai gal ga2 ga3 proved that any compact oriented irreducible 3 manifold with nonzero first betti number has many reebless finite depth foliations roughly a

a survey of the near field far field inverse scattering inverse source integral equation the kirchhoff direct integration of the scalar wave equation is reviewed and some properties of the kirchhoff surface integral are discussed from the perspective of the inverse scattering inverse source problem a modified kirchhoff surface integral is introduced leading to a fredholm integral equation of the first kind for the unknown sources induced by the incident field inside a volume in terms of the scattered fields on the surface enclosing this volume the properties and physical meaning of this integral equation are discussed a generalization of this integral equation for the vector electromagnetic wave equations is presented

embeddedness of minimal surfaces with total boundary curvature at most 4 pi this paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 47r must be smoothly embedded related results are proved for varifolds and for soap film surfaces

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

the realization problem for linear periodic systems abstract the realization problem for discrete time linear periodic systems is considered deep insight on the various complicated aspects of minimal quasi minimal and uniform realization is provided based on the knowledge of the structural properties of discrete time periodic systems the results hinge on the lifting isomorphism between such systems and time invariant ones

characteristic subsurfaces and dehn filling let m be a simple knot manifold using the characteristic submanifold theory and the combinatorics of graphs in surfaces we develop a method for bounding the distance between the boundary slope of an essential surface in m which is not a fiber or a semi fiber and the boundary slope of a certain type of singular surface applications include bounds on the distances between exceptional dehn surgery slopes it is shown that if the fundamental group of m has no non abelian free subgroup and if m is a reducible manifold which is not homeomorphic to s 1 s 2 or p 3 p 3 then 5 under the same condition on m it is shown that if m is seifert fibered then 6 moreover in the latter situation character variety techniques are used to characterize the topological types of m and m in case the bound of 6 is attained

variable background born inversion by wavefield backpropagation the inverse scattering problem for an acoustic medium is formulated by using the variable background born approximation a constant density acoustic medium is probed by a wide band point source and the scattered field is observed along a curved receiver array located outside the region where the medium velocity is different from the assumed background velocity function the solution proposed relies on the introduction of a backpropagated field this field is obtained by using a finite difference scheme backward in time to backpropagate into the medium the scattered field observed along the receiver array the backpropagated field is imaged at the source travel times giving an image of the same type as obtained by reverse time finite difference migration techniques the gradient of this image is then taken along rays linking the source to points in the medium and after scaling this gives the reconstructed potential to relate the reconstructed potential to the true scattering potential high frequency

on k hulls and related problems for any set x of points in any dimension and any k 1 2 cdots we introduce the concept of the k hull of x the k hull is the set of points p such that for any hyperplane containing p there

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

the maximal number of exceptional dehn surgeries thurston s hyperbolic dehn surgery theorem is one of the most important results in 3 manifold theory and it has stimulated an enormous amount of research if m is a compact orientable hyperbolic 3 manifold with boundary a single torus then the theorem asserts that for all but finitely many slopes s on m the manifold m s obtained by dehn filling along s also admits a hyperbolic structure the slopes s where m s is not hyperbolic are known as exceptional a major open question has been what is the maximal number of exceptional slopes on such a manifold m when m is the exterior of the figure eight knot the number of exceptional slopes is 10 and this was conjectured by gordon in 19 to be an upper bound that holds for all m in this paper we prove this conjecture

the contact invariant in sutured floer homology we describe an invariant of a contact 3 manifold with convex boundary as an element of juhasz s sutured floer homology our invariant generalizes the contact invariant in heegaard floer homology in the closed case due to ozsvath and szabo

heegaard splittings of seifert fibered spaces with boundary we give the classification theorem for heegaard splittings of fiberwise orientable seifert fibered spaces with nonempty boundary a thin position argument yields a reducibility result which by induction shows that all heegaard splittings of such manifolds are vertical in the sense of lustig moriah algebraic arguments allow a classification of the vertical heegaard splittings

exceptional and cosmetic surgeries on knots we show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and heegaard surfaces in the manifolds that result from non trivial dehn surgeries on the knot in particular knots with high bridge distance do not admit non trivial non hyperbolic surgeries or non trivial cosmetic surgeries we further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of seifert genus or indeed by the genus of almost any essential surface or heegaard surface in the surgered manifold

structural properties of multirate sampled data systems a complete analysis of the structural properties of multirate sampled data systems is considered in this paper necessary and sufficient conditions for the reachability controllability and stabilizability and for the dual notions are given in terms of simple rank tests these results obtained by the structural theory of periodic systems generalize to the multirate case the well known conditions of the single rate case

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

new perspectives on self linking abstract we initiate the study of classical knots through the homotopy class of the nth evaluation map of the knot which is the induced map on the compactified n point configuration space sending a knot to its nth evaluation map realizes the space of knots as a subspace of what we call the nth mapping space model for knots we compute the homotopy types of the first three mapping space models showing that the third model gives rise to an integer valued invariant we realize this invariant in two ways in terms of collinearities of three or four points on the knot and give some explicit computations we show this invariant coincides with the second coefficient of the conway polynomial thus giving a new geometric definition of the simplest finite type invariant finally using this geometric definition we give some new applications of this invariant relating to quadrisecants in the knot and to complexity of polygonal and polynomial realizations of a knot

heegaard floer homology and fibred 3 manifolds given a closed 3 manifold y we show that the heegaard floer homology determines whether y fibres over the circle with a fibre of negative euler characteristic this is an analogue of an earlier result about knots proved by ghiggini and the author

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

heegaard floer homology and concordance bounds on the thurston norm we prove that twisted correction terms in heegaard floer homology provide lower bounds on the thurston norm of certain cohomology classes determined by the strong concordance class of a 2 component link l in s 3 we then specialise this procedure to knots in s 2 times s 1 and obtain a lower bound on their geometric winding number furthermore we produce an obstruction for a knot in s 3 to have untwisting number 1 we then provide an infinite family of null homologous knots with increasing geometric winding number on which the bound is sharp

distance between toroidal surgeries on hyperbolic knots in the 3 sphere for a hyperbolic knot in the 3 sphere at most finitely many dehn surgeries yield non hyperbolic 3 manifolds as a typical case of such an ex ceptional surgery a toroidal surgery is one that yields a closed 3 manifold containing an incompressible torus the slope corresponding to a toroidal surgery called a toroidal slope is known to be integral or half integral we show that the distance between two integral toroidal slopes for a hyperbolic knot except the figure eight knot is at most four

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

sutured floer homology fibrations and taut depth one foliations for an oriented irreducible 3 manifold m with non empty toroidal boundary we describe how sutured floer homology sfh can be used to determine all fibred classes in h 1 m furthermore we show that the sfh of a balanced sutured manifold m gamma detects which classes in h 1 m admit a taut depth one foliation such that the only compact leaves are the components of r gamma the latter had been proved earlier by the first author under the extra assumption that h 2 m 0 the main technical result is that we can obtain an extremal spin c structure s i e one that is in a corner of the support of sfh via a nice and taut sutured manifold decomposition even when h 2 m not equal 0 assuming the corresponding group sfh m gamma s has non trivial euler characteristic

obstructing pseudoconvex embeddings and contractible stein fillings for brieskorn spheres abstract a question in low dimensional symplectic topology asks whether every compact contractible 4 manifold admits the structure of a stein domain a related conjecture due to gompf asserts that no nontrivial brieskorn homology sphere admits a pseudoconvex embedding in c 2 with either orientation we give the first known example of a contractible boundary irreducible 4 manifold that admits no stein structure with either orientation though its boundary has stein fillings with both orientations we also verify gompf s conjecture with one orientation for a family of brieskorn spheres of which some are known to admit a smooth embedding in c 2 a byproduct of our example is the construction of a cork that does not admit a stein structure with either orientation

dehn fillings of large hyperbolic 3 manifolds let m be a compact connected orientable hyperbolic 3 manifold whose boundary is a torus and which contains an essential closed surface s i t is conjectured that 5 is an upper bound for the distance between two slopes on m whose associated fillings are not hyperbolic manifolds in this paper we verify the conjecture when the first betti number of m is at least 2 by showing that given a pseudo anosov mapping class f of a surface and an essential simple closed curve in the surface then 5 is an upper bound for the diameter of the set of integers n for which the composition of f with the n th power of a dehn twist along is not pseudo anosov this sharpens an inequality of albert fathi for large manifolds m of first betti number 1 we obtain partial results set

a characterization of virtually embedded subsurfaces in 3 manifolds this paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3 manifold which generalizes an invariant due to rubinstein and wang the subsurface is virtually embedded if and only if the almost fiber part is aspiral and in this case the subsurface is virtually a leaf of a taut foliation besides other consequences examples are exhibited that nongeometric 3 manifolds with no seifert fibered pieces may contain essentially immersed but not virtually embedded closed subsurfaces

the second hull of a knotted curve the convex hull of a set k in space consists of points which are in a certain sense su rrounded by k when k is a closed curve we define its higher hulls consisting of po ints which are multiply surrounded by the curve our main theorem shows that if a curve is knotted then it has a nonempty second hull this provides a new proof of the fary milnor theorem that every knotted curve has total curvature at least 4 a space curve must loop around at least twice to become knotted this intuitive idea was captured in the celebrated fary milnor theorem which says the total curvature of a knot ted curve k is at least 4 we prove a stronger result that there is a certain region of space doubly enclosed in a preci se sense by k we call this region the second hull of k the convex hull of a connected set k is characterized by the fact that every plane through a point in the hull must in teresect k if k is a closed curve then a generic plane inter sects k an even number of times so the convex hull is the set of points through which every plane cuts k twice extending this we introduce a definition which measures the degree to which points are enclosed by k a point p is said to be in the n th hull of k if every plane through p intersects k at least 2n times a space curve is convex and planar if and only if it has the two piece property every plane cuts it into at most two pieces this has been generalized by kuiper among others see cc97 in the study of tight and taut submanifolds it was milnor mil50 who first observed that for a knotted curve there are planes in every direction which cut it four times our main theorem strengthens this to find points through which every plane cuts the knot four times more precisely it says that any curve k with a knotted inscribed polygon in particular any knotted curved of finite total curvature has a nonempty second hull as shown for a trefoil in figure 1 fur thermore in a certain sense this hull must extend across th e knot using quadrisecants we get an alternate approach to second hulls and in particular we show that the second hull of a generic prime knot k is not contained in any embedded normal tube aroundk we use some ideas from integral geometry to show that the total curvature of a space curve with nonempty n th hull is at least 2 n thus our theorem provides an alternate proof of the fary milnor theorem we do not yet know any topological knot type which is guaranteed to have a nonempty third hull though we suspect that this is true for the 3 4 torus knot see figure 5 it w ould

norms on the cohomology of hyperbolic 3 manifolds we study the relationship between two norms on the first cohomology of a hyperbolic 3 manifold the purely topological thurston norm and the more geometric harmonic norm refining recent results of bergeron engun and venkatesh as well as older work of kronheimer and mrowka we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3 manifold itself moreover we give families of examples showing that some but not all qualitative aspects of our estimates are sharp finally we exhibit closed hyperbolic 3 manifolds where the thurston norm grows exponentially in terms of the volume and yet there is a uniform lower bound on the injectivity radius

unknotting tunnels and seifert surfaces let k be a knot with an unknotting tunnel gamma and suppose that k is not a 2 bridge knot there is an invariant rho p q in mathbb q 2 mathbb z with p odd defined for the pair k gamma the invariant rho has interesting geometric properties it is often straightforward to calculate for example for k a torus knot and gamma an annulus spanning arc rho k gamma 1 although rho is defined abstractly it is naturally revealed when k cup gamma is put in thin position if rho neq 1 then there is a minimal genus seifert surface f for k such that the tunnel gamma can be slid and isotoped to lie on f one consequence is that if rho k gamma neq 1 then mathrm genus k 1 this confirms a conjecture of goda and teragaito for pairs k gamma with rho k gamma neq 1

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

pseudo isotopies of irreducible 3 manifolds it is shown that a certain subspace of the space of all pseudo isotopies of any irreducible 3 manifold is connected this subspace consists of those pseudo isotopies corresponding to 1 parameter families of functions which have nondegenerate critical points of index 1 and 2 only and which contain no slides among the 2 handles some of the techniques developed are used to prove a weak four dimensional h cobordism theorem

dehn surgery on knots in 3 manifolds it has been known for over 30 years that every closed connected orientable 3manifold is obtained by surgery on a link in s3 8 however a classification of such 3 manifolds in terms of this surgery construction has remained elusive this is due primarily to the lack of uniqueness of the surgery description in 5 kirby gave us a calculus of surgery diagrams however the lack of a canonical surgical method of getting from one 3 manifold to another has hampered further progress in this paper we show that if one restricts attention to the case where a surgery curve is homotopically trivial in a 3 manifold then one has the following uniqueness theorem

sutured manifold hierarchies essential laminations and dehn surgery x0 introduction a compact orientable surface f with nonnegative euler characteristic is either a sphere a disk a torus or an annulus if a 3 manifold m contains such an essential surface then it is said to be reducible reducible toroidal or annular respectively any such surface can be used to decompose the manifold further into simpler manifolds we say that m is a simple manifold if it has no such surfaces a simple manifold is expected to have a nice geometric structure if m has nonempty boundary then the geometrization theorem of thurston for haken manifolds says that m with boundary tori removed admits a nite volume hyperbolic structure with totally geodesic boundary when m has no boundaries thurston s geometrization conjecture asserts that m is either hyperbolic or is a seifert b er space with orbifold a sphere with at most 3 cone points suppose t is a torus boundary component of m we use m to denote the manifold obtained by dehn lling on t so that the slope on t bounds a disk in the dehn lling solid torus when m e k is the exterior of a knot k in s 3 denote m by k and call it the manifold obtained by surgery on the knot k it is well known that if m is simple then there are only nitely many dehn llings on t which produce non simple manifolds if m 1 and m 2 are non simple manifolds then the geometric intersection number between 1 and 2 denoted by 1 2 is proved to be at most 8 by gordon gor1 there are 10 dieren t cases according to the types of nonnegative euler characteristic surfaces in m i in many cases the upper bounds for 1 2 have been established see table 0 1

knot floer homology detects genus one fibred knots ozsv ath and szab o conjectured that knot floer homology detects fibred knots we propose a strategy to approach this conjecture based on contact topology and gabai s theory of sutured manifold decomposition we implement this strategy for genus one knots obtaining as a corollary that if rational surgery on a knot k gives the poincar e homology sphere sigma 2 3 5 then k is the left handed trefoil knot

the topology of symplectic circle bundles we consider circle bundles over compact three manifolds with symplectic total spaces we show that the base of such a space must be irreducible or the product of the two sphere with the circle we then deduce that such a bundle admits a symplectic form if and only if it admits one that is invariant under the circle action in three special cases namely if the base is seifert bered has vanishing thurston norm or if the total space admits a lefschetz bration

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented

quantum deformations of fundamental groups of oriented 3 manifolds we compute two term skein modules of framed oriented links in oriented 3 manifolds they contain the self writhe and total linking number invariants of framed oriented links in a universal way the relations in a natural presentation of the skein module are interpreted as monodromies in the space of immersions from circles to the 3 manifold