knot concordance whitney towers and l 2 signatures we construct many examples of nonslice knots in 3 space that cannot be distinguished from slice knots by previously known invariants using whitney towers in place of embedded disks we define a geometric filtration of the 3 dimensional topological knot concordance group the bottom part of the filtration exhibits all classical concordance invariants including the cassongordon invariants as a first step we construct an infinite sequence of new obstructions that vanish on slice knots these take values in the l theory of skew fields associated to certain universal groups finally we use the dimension theory of von neumann algebras to define an l 2 signature and use this to detect the first unknown step in our obstruction theory

curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

a controlled plus construction for crumpled laminations given a closed n manifold m n 4 and a finitely generated perfect subgroup p of it1 m we previously developed a controlled version of quillen s plus construction namely a cobordism w m n with the inclusion j n f w a homotopy equivalence and kernel of i i1 m f it1 w equalling the smallest normal subgroup of xl1 m containing p together with a closed map p w 0 1 such that p l t is a closed n manifold for every t e 0 1 and in particular m p 1 o and n p l l we accomplished this by constructing an acyclic map of manifolds f m f n having the right fundamental groups and w arose as the mapping cylinder of f with a collar attached along n the main result here presents a condition under which the desired controlled plus construction can still be accomplished in many cases even when it1 m contains no finitely generated perfect subgroups by products of these results include a new method for constructing wild embeddings of codimension one manifolds and a better understanding of perfect subgroups of finitely presented groups

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

simply connected 4 manifolds with a given boundary let m be a closed oriented connected 3 manifold for each bilinear symmetric pairing zn l our goal is to calculate the set vl m of all oriented homeomorphism types of compact 1 connected oriented 4manifolds with boundary m and intersection pairing isomorphic to zn l for each pair zn l which presents h m we construct a double coset space bl m and a function ct vl m bl m the set bt m is the quotient of the group of all link pairing preserving isomorphisms of the torsion subgroup of h1 m by two naturally occuring subgroups when zn l is an even pairing we construct another double coset space bl m a function 6l vl m b fl m and a projection p2 bl m bl m such that p2 c l ct our main result states that when zn l is even the function c l is injective as is the function c x a vl m bl m x z 2 when z l is odd here a is a kirby siebenmann obstruction to smoothing it follows that the sets vl m are finite and of an order bounded above by a constant depending only on h1 m we also show that when hi m q 0 and z l is even ct p2 c 6l is injective it seems likely that via the functions cl x a and 6l the sets bl m x z 2 and bl m calculate vl m when zn l is respectively odd and even we verify this in several cases most notably when h1 m is free abelian the results above are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between two 1connected 4 manifolds extending a given homeomorphism of their boundaries the theory developed is then applied to show that there is an m 0 depending only on h1 m such that for any self homeomorphism f of m fm extends to a self homeomorphism of any 1 connected compact 4 manifold with boundary m introduction in m freedman s fundamental paper fr he classified closed simply connected oriented 4 manifolds up to orientation preserving homeomorphism he showed that modulo the kirby siebenmann invariant these manifolds are in bijective correspondence through their intersection pairings with the set of unimodular bilinear symmetric pairings over z see theorem 1 5 of fr and corollary 2 2 3 of q in this paper we begin a classification of simply connected 4 manifolds with connected boundary our results with regard to this problem are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between 1 connected 4 manifolds extending a given homeomorphism of their boundaries received by the editors september 19 1985 1980 mathematics subject classification 1985 revision primary 57n15 research supported by an nserc canada post doctoral fellowship 1986 american mathematical society 0002 9947 86 1 00 25 per page

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

property t discrete quantum groups and subfactors with triangle presentations abstract kazhdan s property t has been studied for several discrete group like structures including standard invariants of jones subfactors and discrete quantum groups we prove a uk type spectral gap criterion for property t in this setting this allows us to construct a family of property t discrete quantum groups as well as subfactor standard invariants given by generators and a triangle presentation these are the first examples of property t discrete quantum groups that are not directly related to a discrete group with property t

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

distributed fusion estimation with square root array implementation for markovian jump linear systems with random parameter matrices and cross correlated noises the distributed fusion estimation is presented for markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the lmmse estimator is derived based on gram schmidt orthogonal innovation sequence under a centralized framework the square root array implementation is further presented by recursively triangularizing the square roots of related positive semidefinite matrices in the lmmse estimator via the information filter form the distributed fusion estimation with square root array implementation is proposed incorporated with consensus strategy the convergent condition and the convergence point are also discussed with respect to consensus strategy this study presents the distributed fusion estimation of discrete time markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the recursive linear minimum mean square error estimator is proposed based on the gram schmidt orthogonalization procedure under a centralized framework in order to avoid the loss of positive semidefiniteness and reduce dynamical range its square root array implementation is presented by recursively triangularizing the square roots of relevant positive semidefinite matrices furthermore via the information filter form the distributed fusion estimation with square root array implementation is derived from the centralized fusion structure incorporated with consensus strategy a maneuvering target tracking simulation in a sensor network validates the proposed method

drinfeld center and representation theory for monoidal categories motivated by the relation between the drinfeld double and central property t for quantum groups given a rigid c tensor category mathcal c and a unitary half braiding on an ind object we construct a representation of the fusion algebra of mathcal c this allows us to present an alternative approach to recent results of popa and vaes who defined c algebras of monoidal categories and introduced property t for them as an example we analyze categories mathcal c of hilbert bimodules over a ii1 factor we show that in this case the drinfeld center is monoidally equivalent to a category of hilbert bimodules over another ii1 factor obtained by the longo rehren construction as an application we obtain an alternative proof of the result of popa and vaes stating that property t for the category defined by an extremal finite index subfactor n subset m is equivalent to popa s property t for the corresponding se inclusion of ii1 factors in the last part of the paper we study muger s notion of weakly monoidally morita equivalent categories and analyze the behavior of our constructions under the equivalence of the corresponding drinfeld centers established by schauenburg in particular we prove that property t is invariant under weak monoidal morita equivalence

heegaard floer homology of matsumoto s manifolds abstract we consider a homology sphere m n k 1 k 2 presented by two knots k 1 k 2 with linking number 1 and framing 0 n we call the manifold matsumoto s manifold we show that m n t 2 3 k 2 never bounds any contractible 4 manifold if n 2 k 2 holds we also give a formula of ozsvath szabo s invariant as the total sum of the euler numbers of the reduced filtration we compute the invariants of the twisted whitehead doubles of torus knots and correction terms of the branched covers of the whitehead doubles by using owens and strle s obstruction we show that the 12 twisted whitehead double of the 2 7 torus knot and the 20 twisted whitehead double of the 3 7 torus knot are not slice but the double branched covers bound rational homology 4 balls these are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4 ball

on applicability of the interacting multiple model approach to state estimation for systems with sojourn time dependent markov model switching in this paper the attempt at the interacting multiple model imm method extension to the state estimation problem with semi markov sojourn time dependent markov stdm system model switching is analyzed it is demonstrated that such an stdm imm approach does not properly take into account the specific character of the stdm switching in the system and it becomes a reason for the reduction of estimation accuracy for this problem it is shown that a hypotheses merging should be restricted in such a way that not only the current system model but also the sojourn time in the model should be given in hypotheses to be tested some other aspects of bayesian estimation in a switching environment are also discussed

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

a new multiple model filter with switch time conditions the interacting multiple model filter has long been the method of choice for performing target tracking using multiple motion models the filter finds a suboptimal solution to a problem which has the implicit assumption that immediate model shifts have the highest probability when the sampling rate of the underlying continuous process is high compared to the target dynamics this is not a reasonable assumption instead changes in dynamics persist for some time in this paper we propose an alternative switching model which forces the dynamic models to persist for at least a model specific time the model is semi markov in nature with a sojourn time probability mass function which is zero for a model specific number of time steps and then follows a geometrical distribution through this assumption a less complex problem in terms of model hypotheses arises and to that problem we derive a state estimation algorithm that is close to optimal when the model assumptions are valid three other semi markov based multiple model filters are discussed and compared to in a qualitative sense we also derive a new aircraft motion model for start and termination of turns finally the proposed filter is evaluated on a benchmark scenario for tracking and the results show a performance increase compared to the interacting multiple model imm filter for the trajectories considered

4 manifold topology i subexponential groups the technical lemma underlying the 5 dimensional topologicals cobordism conjecture and the 4 dimensional topological surgery conjecture is a purely smooth category statement about locating 1 null immersions of disks these conjectures are theorems precisely for those fundamental groups good groups where the 1 null disk lemma ndl holds we expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations 1 extension and 2 direct limit the finitely generated groups in this class are amenable and no amenable group is known to lie outside this class

annular representation theory for rigid c tensor categories abstract we define annular algebras for rigid c tensor categories providing a unified framework for both ocneanu s tube algebra and jones affine annular category of a planar algebra we study the representation theory of annular algebras and show that all sufficiently large full annular algebras for a category are isomorphic after tensoring with the algebra of matrix units with countable index set hence have equivalent representation theories annular algebras admit a universal c algebra closure analogous to the universal c algebra for groups these algebras have interesting corner algebras indexed by some set of isomorphism classes of objects which we call centralizer algebras the centralizer algebra corresponding to the identity object is canonically isomorphic to the fusion algebra of the category and we show that the admissible representations of the fusion algebra of popa and vaes are precisely the restrictions of arbitrary non degenerate representations of full annular algebras this allows approximation and rigidity properties defined for categories by popa and vaes to be interpreted in the context of annular representation theory this perspective also allows us to define higher weight approximation properties based on other centralizer algebras of an annular algebra using the analysis of annular representations due to jones and reznikoff we identify all centralizer algebras for the tlj categories for 2

4 manifold topology ii dwyer s filtration and surgery kernels even when the fundamental group is intractable i e not good many interesting 4 dimensional surgery problems have topological solutions we unify and extend the known examples and show how they compare to the presumed counterexamples by reference to dwyer s filtration on second homology the development brings together many basic results on the nilpotent theory of links as a special case a class of links only slightly smaller than homotopically trivial links is shown to have free slices on their whitehead doubles

surgery in dimension four and noncompact 5 manifolds this paper describes a precise relationship between the problems of completing surgery in dimension four and finding boundaries for noncompact 5 manifolds two outstanding problems of low dimensional topology are completing 4 dimensional surgery and finding boundaries for noncompact 5 dimensional manifolds although no complete theory is known for either problem some interesting results have been found see 1 4 5 10 and addendum in this paper we describe a complete relationship between these two problems consequently knowledge of 4 dimensional surgery yields information about noncompact 5 manifolds and conversely all manifolds and maps in this paper are assumed to be smooth each manifold is provided with a basepoint and when appropriate basepaths will be chosen to given 2 spheres without explicit mention i wish to thank gerald a anderson and frank quinn for helpful discussions also i wish to thank patrick gilmer for his advice and encouragement during this project 1 statement of results let f b m am y x be a degree one normal map in the sense of wall 11 where m is a compact connected 4 manifold and y x is a poincare pair not necessarily simple if x 0 then we require that f jam am x induces an isomorphism of homology groups with a z vi y coefficients also we assume that f is 2 connected k2 m is a free a module and the surgery obstruction a f b e lh 7 c is zero if h c k2 m is a subkernel we will say that h is representable in m if we can find disjoint framed embedded 2 spheres si sr c int m such that the inclusion m ui si m induces an isomorphism of fundamental groups and the classes of sl sr in h2 m a 7t2 m form a basis over a for h the subkernel h is stably representable if for some integer k 0 h ed kei ek is representable in m k s2 x s2 here ei denotes the class of s2 x 1 c ith summand s2 x s2 and e1 ek is the submodule generated by el ek we regard h ed ke ek as received by the editors august 10 1982 1980 mathematics subject classification primary 57r65 secondary 57m99 1985 american mathematical society 0002 9947 85 1 00 25 per page

higher order intersections in low dimensional topology we show how to measure the failure of the whitney move in dimension 4 by constructing higher order intersection invariants of whitney towers built from iterated whitney disks on immersed surfaces in 4 manifolds for whitney towers on immersed disks in the 4 ball we identify some of these new invariants with previously known link invariants such as milnor sato levine and arf invariants we also define higher order sato levine and arf invariants and show that these invariants detect the obstructions to framing a twisted whitney tower together with milnor invariants these higher order invariants are shown to classify the existence of twisted whitney towers of increasing order in the 4 ball a conjecture regarding the nontriviality of the higher order arf invariants is formulated and related implications for filtrations of string links and 3 dimensional homology cylinders are described

whitney towers and gropes in 4 manifolds many open problems and important theorems in low dimensional topology have been formulated as statements about certain 2 complexes called gropes this paper describes a precise correspondence between embedded gropes in 4 manifolds and the failure of the whitney move in terms of iterated towers of whitney disks the flexibility of these whitney towers is used to demonstrate some geometric consequences for knot and link concordance connected to n solvability k cobordism and grope concordance the key observation is that the essential structure of gropes and whitney towers can be described by embedded unitrivalent trees which can be controlled during surgeries and whitney moves it is shown that a whitney move in a whitney tower induces an ihx jacobi relation on the embedded trees

the global structure of simple space times according to a standard definition of penrose a space time admitting well defined future and past null infinitiesi andi is asymptotically simple if it has no closed timelike curves and all its endless null geodesics originate fromi and terminate ati the global structure of such space times has previously been successfully investigated only in the presence of additional constraints the present paper deals with the general case it is shown thati is diffeomorphic to the complement of a point in some contractible open 3 manifold the strongly causal regioni0 ofi is diffeomorphic to mathbb s 2 times mathbb r and every compact connected spacelike 2 surface ini is contained ini0 and is a strong deformation retract of bothi0 andi moreover the space time must be globally hyperbolic with cauchy surfaces which subject to the truth of the poincare conjecture are diffeomorphic to 3

cobordism for links in we give an explicit finite set of based links which generates under connected sum the k cobordism classes of links we show that the union of these generating sets 2 1 and in this case c m does not appear to have a natural group structure moreover we consider only linking properties as opposed to knotting of the individual components of the link the invariants we consider are independent of the concordance class of the component knots our links are oriented ordered and tame weaker equivalence relations have recently been considered by n sato k orr and the author sa 02 c2 c3 let us immediately generalize these in order to state our main results definition 1 1 a link l l1 l 1 in 53 is b1 bm cobordant to l l1 l4 where bi are ordinal numbers if there are disjointly embedded compact connected oriented surfaces vi in 53 x 0 1 such that i vi n s3 x o 1 a vi a vi ii a vil where l vio l and d vil received by the editors august 10 1989 1980 mathematics subject classification 1985 revision primary 57m25 secondary 55s30

state estimation for systems with sojourn time dependent markov model switching a switching process in which the switching probabilities depend on a random sojourn time is a class of semi markov processes and is encountered in target tracking systems subject to failures and also in the socioeconomic environment in such a system knowledge of the sojourn time is needed for the computation of the conditional transition probabilities it is shown how one can infer the transition probabilities through the evaluation of the conditional distribution of the sojourn time subsequently a recursive state estimation for such systems is obtained using the conditional sojourn time distribution for dynamic systems with imperfect observations and changing structures models

a family of freely slice good boundary links we show that every good boundary link with a pair of derivative links on a seifert surface satisfying a homotopically trivial plus assumption is freely slice this subsumes all previously known methods for freely slicing good boundary links with two or more components and provides new freely slice links

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

rational whitney tower filtration of links we present complete classifications of links in the 3 sphere modulo framed and twisted whitney towers in a rational homology 4 ball this provides a geometric characterization of the vanishing of the milnor invariants of links in terms of whitney towers our result also says that the higher order arf invariants which are conjectured to be nontrivial measure the potential difference between the whitney tower theory in rational homology 4 balls and that in the 4 ball extensively developed by conant schneiderman and teichner

stable mapping class groups of 4 manifolds with boundary we give a complete algebraic description of the mapping class groups of compact simply connected 4 manifolds with boundary up to connected sum with copies of s 2 s 2

irreducible unitary representations of quantum lorentz group a complete classification of irreducible unitary representations of a one parameter deformations q l 2 c 0 q 1 ofsl 2 c is given it shows that in spite of a popular belief the representation theory fors q l 2 c is not a smooth deformation of the one forsl 2 c

construction of group actions on four manifolds it is shown that any cyclic group of odd prime order acts on any closed simply connected topological 4 manifold inducing the identity on integral homology the action is locally linear except perhaps at one isolated fixed point in the case of primes greater than three a more careful argument is used to show that the action can be constructed to be locally linear introduction in this paper we shall show that every closed simply connected topological 4 manifold m4 admits an action of any cyclic group zp of odd prime order p the action will be homologically trivial that is induce the identity on integral homology be pseudofree that is have only isolated fixed points except in certain cases when p 3 and be locally linear except perhaps at one isolated fixed point when p 2 and the intersection form of m4 has even type then the same conclusion holds this is also due to s kwasik and p vogel 1985 by a somewhat different proof if p 2 and the intersection form of m has odd type however then an action of z2 which is homologically trivial must have a fixed point set containing two dimensional components see 7 further it is harder to control the kirby siebenmann triangulation obstruction which is then not determined by the intersection form it is interesting to ask whether these actions can be locally linear or smooth when m4 is smooth the existence of a locally linear z2 action implies the vanishing of the kirby siebenmann obstruction see kwasik and vogel 1984 we shall show however that for p 3 in general these actions can be constructed to be locally linear in a recent preprint kwasik has shown that this is the case for the fake cp2 when p is odd by a rather different proof these actions are homologically trivial and have only isolated fixed points except sometimes when p 3 the g signature theorem shows that not every simply connected 4 manifold admits pseudofree locally linear actions when p 3 we shall see for example that neither the e8 manifold the kummer surface nor a nontrivial connected sum of copies of cp2 admits such an action for p 3 in broad outline our construction goes as follows let a closed oriented simply connected 4 manifold m be given by studying equivariant framed links we construct a compact smooth 4 manifold with boundary having the intersection form of m and admitting a smooth zp action which is pseudofree and homologically trivial the action is free on the boundary homology sphere e in a paper primarily focused on equivariant plumbing diagrams for high dimensional highly connected manifolds with even intersection forms weintraub 1975 carried out most of this we give an independent development because we need to be able to better control received by the editors october 16 1985 and in revised form january 7 1986 1980 mathematics subject classification 1985 revision primary 57s17 57s25 57n15 research supported in part by a grant from the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

comparison of unitary duals of drinfeld doubles and complex semisimple lie groups we determine a substantial part of the unitary representation theory of the drinfeld double of a q deformation of a compact lie group in terms of the complexification of the compact lie group using this we show that the dual of every q deformation of a higher rank compact lie group has central property t we also determine the unitary dual of sl q n mathbb c

a surgery sequence in dimension four the relations with knot concordance we present a systematic treatment of the classification problem for compact smooth 4 manifolds m it is modeled on the surgery exact sequence the central theorem in the classification of n manifolds n 5 the price for the extension to dimension 4 is a hole in m where a homotopy 1 skeleton should be there is no homotopy theoretic or surgical obstruction to complet ing m with a wedge of circles so that the completion has the topology of a compact smooth manifold this point set problem is all that stands between 4 manifolds and the tranquility that prevails in higher dimensions when m is simply connected only a point is missing from the model the applications of this are discussed in f and fq 1 the general theory has application to knot and link theory in particular knots with alexander polynomial 1 are characterized geometrically as knots admitting a certain

linking and causality in globally hyperbolic space times the classical linking number lk is defined when link components are zero homologous in 15 we constructed the affine linking invariant alk generalizing lk to the case of linked submanifolds with arbitrary homology classes here we apply alk to the study of causality in lorentzian manifolds

a diffeomorphism classification of manifolds which are like projective planes we give a complete diffeomorphism classification of 1 connected closed manifolds m with integral homology h m z z z provided that dim m 6 4

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4