the coarse baum connes conjecture via c0 coarse geometry the c0 coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space in this paper we will prove the c0 version of the coarse baum connes conjecture and show that k c x0 is a topological invariant for a broad class of metric spaces using this result we construct a geometric obstruction group to the coarse baum connes conjecture for the bounded coarse structure we then show under the assumption of finite asymptotic dimension that the obstructions vanish and hence we obtain a new proof of the coarse baum connes conjecture in this context

the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

extended kepler coulomb quantum superintegrable systems in three dimensions the quantum kepler coulomb system in three dimensions is well known to be second order superintegrable with a symmetry algebra that closes polynomially under commutators this polynomial closure is also typical for second order superintegrable systems in 2d and for second order systems in 3d with nondegenerate four parameter potentials however the degenerate three parameter potential for the 3d kepler coulomb system also second order superintegrable is an exception as its symmetry algebra does not close polynomially the 3d four parameter potential for the extended kepler coulomb system is not even second order superintegrable but verrier and evans 2008 j math phys 49 022902 showed it was fourth order superintegrable and tanoudis and daskaloyannis 2011 arxiv 11020397v1 showed that if a second fourth order symmetry is added to the generators the symmetry algebra closes polynomially here based on the tremblay turbiner and winternitz construction we consider an infinite class of quantum extended kepler coulomb three and four parameter systems indexed by a pair of rational numbers k1 k2 and reducing to the usual systems when k1 k2 1 we show these systems to be superintegrable of arbitrarily high order and determine the structure of their symmetry algebras we demonstrate that the symmetry algebras close algebraically only for systems admitting extra discrete symmetries is polynomial closure achieved underlying the structure theory is the existence of raising and lowering operators not themselves symmetry operators or even defined independent of basis that can be employed to construct the symmetry operators and their structure relations

cyclic cohomology and higher indexes for noncompact complete manifolds abstract the indices of generalized dirac operators on noncompact complete riemannian manifolds live in the k theory of uniform roe algebras in this paper we shall compute the cyclic cohomology of uniform roe algebras associated to noncompact manifolds the cyclic cohomology of the uniform roe algebras is identified with uniform simplical cohomology with infinite support of the rips polyhedrons associated to a net of the riemannian manifold we also compute the chern character of the k theoretic indices of generalized dirac operators we apply such a computation to the analysis and geometry of noncompact complete riemannian manifolds in particular we show that a uniformly contractible riemnannian manifold with bounded geometry cannot have uniform positive scalar curvature outside a compact set if the volume and contractibility radius have certain subexponential growth

generalized lenard chains separation of variables and superintegrability we show that the notion of generalized lenard chains naturally allows formulation of the theory of multiseparable and superintegrable systems in the context of bi hamiltonian geometry we prove that the existence of generalized lenard chains generated by a hamiltonian function defined on a four dimensional n manifold guarantees the separation of variables as an application we construct such chains for the henon heiles systems and for the classical smorodinsky winternitz systems new bi hamiltonian structures for the kepler potential are found

superintegrability and higher order integrals for quantum systems we refine a method for finding a canonical form of symmetry operators of arbitrary order for the schrodinger eigenvalue equation h 2 v e on any 2d riemannian manifold real or complex that admits a separation of variables in some orthogonal coordinate system the flat space equations with potentials v x iy k 1 x iy k 1 in cartesian coordinates and v r2 r2cos 2k r2sin 2k the tremblay turbiner and winternitz system in polar coordinates have each been shown to be classically superintegrable for all rational numbers k we apply the canonical operator method to give a constructive proof that each of these systems is also quantum superintegrable for all rational k we develop the classical analog of the quantum canonical form for a symmetry it is clear that our methods will generalize to other hamiltonian systems

classical and quantum superintegrability with applications a superintegrable system is roughly speaking a system that allows more integrals of motion than degrees of freedom this review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta we present a classification of second order superintegrable systems in two dimensional riemannian and pseudo riemannian spaces it is based on the study of the quadratic algebras of the integrals of motion and on the equivalence of different systems under coupling constant metamorphosis the determining equations for the existence of integrals of motion of arbitrary order in real euclidean space e2 are presented and partially solved for the case of third order integrals a systematic exposition is given of systems in two and higher dimensional space that allow integrals of arbitrary order the algebras of integrals of motions are not necessarily quadratic but close polynomially or rationally the relation between superintegrability and the classification of orthogonal polynomials is analyzed

a new superintegrable hamiltonian we identify a new superintegrable hamiltonian in three degrees of freedom obtained as a reduction of pure keplerian motion in six dimensions the new hamiltonian is a generalization of the keplerian one and has the familiar 1 r potential with three barrier terms preventing the particle crossing the principal planes in three degrees of freedom there are five functionally independent integrals of motion and all bound classical trajectories are closed and strictly periodic the generalization of the laplace runge lenz vector is identified and shown to provide functionally independent isolating integrals they are quartic in the momenta and do not arise from separability of the hamilton jacobi equation a formulation of the system in action angle variables is presented

c algebra extension theory and duality we develop a duality theory introduced by paschke to give a simplified account of the main results of the brown douglas fillmore extension theory and the relative k homology theory of baum and douglas

infinite families of superintegrable systems separable in subgroup coordinates a method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly solvable it is shown that in two dimensional euclidean or pseudo euclidean spaces the method also preserves superintegrability two infinite families of classical and quantum superintegrable systems are obtained in two dimensional pseudo euclidean space whose classical trajectories and quantum eigenfunctions are investigated in particular the wave functions are expressed in terms of laguerre and generalized bessel polynomials

master symmetries non hamiltonian symmetries and superintegrability of the generalized smorodinsky winternitz system the first part of the paper is devoted to the theory of master symmetries using the geometric formalism as an approach it is shown that certain superintegrable systems are endowed with this property as a consequence of the existence of a family of master symmetries in the second part the properties of dynamical but non hamiltonian symmetries are studied it is proved that the higher order superintegrability of the generalized smorodinsky winternitz system is a consequence of the existence of symplectic symmetries not preserving the hamiltonian function

a unified treatment of quartic invariants at fixed and arbitrary energy two dimensional hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the jacobi geometrization of the dynamics this approach allows for a unified treatment of invariants at both arbitrary and fixed energy in the differential geometric picture the quartic invariant corresponds to the existence of a fourth rank killing tensor expressing the jacobi metric in terms of a kahler potential the integrability condition for the existence of the killing tensor at fixed energy is a nonlinear equation involving the kahler potential at arbitrary energy further conditions must be imposed which lead to an overdetermined system with isolated solutions we obtain several new integrable and superintegrable systems in addition to all previously known examples

second order superintegrable systems in conformally flat spaces ii the classical two dimensional stackel transform this paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems both classical and quantum in conformally flat spaces here we study the stackel transform or coupling constant metamorphosis as an invertible mapping between classical superintegrable systems on different spaces through the use of this tool we derive and classify for the first time all two dimensional 2d superintegrable systems the underlying spaces are exactly those derived by koenigs in his remarkable paper giving all 2d manifolds with zero potential that admit at least three second order symmetries our derivation is very simple and quite distinct we also show that every superintegrable system is the stackel transform of a superintegrable system on a constant curvature space

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

c0 coarse geometry of complements of z sets in the hilbert cube motivated by the chapman complement theorem we construct an isomorphism between the topological category of compact z sets in the hilbert cube q and the c0 coarse category of their complements the c0 coarse morphisms are in this particular case intrinsically related to uniformly continuous proper maps using that fact we are able to relate in a natural way some of the topological invariants of z sets to the geometry of their complements

completeness of superintegrability in two dimensional constant curvature spaces we classify the hamiltonians h px2 py2 v x y of all classical superintegrable systems in two dimensional complex euclidean space with two additional second order constants of the motion we similarly classify the superintegrable hamiltonians h j12 j22 j32 v x y z on the complex two sphere where x2 y2 z2 1 this is achieved in all generality using properties of the complex euclidean group and the complex orthogonal group

a new approach to the higher order superintegrability of the tremblay turbiner winternitz system the higher order superintegrability of systems separable in polar coordinates is studied using an approach that was previously applied for the study of the superintegrability of a generalized smorodinsky winternitz system the idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions here denoted by m and n this technique leads to a proof of the superintegrability of the tremblay turbiner winternitz system and to the explicit expression of the constants of motion a second family related with the first one of superintegrable systems is also studied

necessary conditions for classical super integrability of a certain family of potentials in constant curvature spaces we formulate the necessary conditions for the maximal super integrability of a certain family of classical potentials defined in the constant curvature two dimensional spaces we give examples of homogeneous potentials of degree 2 on as well as their equivalents on and for which these necessary conditions are also sufficient we show explicit forms of the additional first integrals which can always be chosen as a polynomial with respect to the momenta and which can be of an arbitrary high degree with respect to the momenta

quantitative k theory for banach algebras abstract quantitative or controlled k theory for c algebras was used by guoliang yu in his work on the novikov conjecture and later developed more formally by yu together with herve oyono oyono in this paper we extend their work by developing a framework of quantitative k theory for the class of algebras of bounded linear operators on subquotients i e subspaces of quotients of l p spaces we also prove the existence of a controlled mayer vietoris sequence in this framework

on cyclic q ary images in concatenated form this paper shows that q ary images of some cyclic codes can be put into concatenated form in the sense of jensen 1985 this description utilizes an isomorphism between the gf q algebras gf q z znm 1 and gf q x y xn 1 ym x we also describe an element of the constacyclic outer code which is of great help in determining one of its generator polynomials

the q ary image of a q sup m ary cyclic code for n q 1 v a q sup m ary cyclic code of length n and with generator polynomial g x we show that there exists a basis for f q sup m over f sub q with respect to which the q ary image of v is cyclic if and only if i g x is over f sub q or ii g x g sub 0 x x spl gammasup q spl mu g sub 0 x is over f sub q f sub qspl ne f q sup k f sub q spl gamma spl sub f q sup m spl mu an integer modulo k and w sup m spl gamma has a divisor over f q sup k of degree e m k or iii g x g sub 0 x spl pisub spl muspl epsiv s x spl gamma q sup spl mu g sub 0 x is over f sub q f sub qspl ne f q sup k f sub q spl gamma spl sub f q sup m s a set of integers module k of cardinality k 1 and w sup m spl mu has a divisor over f q sup k of degree e m k in all of the above cases we determine all of the bases with respect to which the q ary image of v is cyclic

unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold in this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the poisson algebra of the integrals of motion there are six general fundamental classes of superintegrable systems analytic formulas for the involved integrals are calculated in all the cases all the known superintegrable systems are classified as special cases of these six general classes

are all classical superintegrable systems in two dimensional space linearizable several examples of classical superintegrable systems in a two dimensional space are shown to possess hidden symmetries leading to their linearization they include those determined fifty years ago in the work of fris et al phys lett 13 354 356 1965 their generalizations and the more recent tremblay turbiner winternitz system f tremblay et al j phys a math theor 42 242001 2009 we conjecture that all classical superintegrable systems in the two dimensional space have hidden symmetries that make them linearizable

higher order superintegrability of separable potentials with a new approach to the post winternitz system the higher order superintegrability of separable potentials is studied it is proved that these potentials possess in addition to the two quadratic integrals a third integral of higher order in the momenta that can be obtained as the product of powers of two particular rather simple complex functions some systems related to the harmonic oscillator such as the generalized sw system and the ttw system were studied in previous papers now a similar analysis is presented for superintegrable systems related to the kepler problem in this way a new proof of the superintegrability of the post winternitz system is presented and the explicit expression for the integral is obtained finally the relations between the superintegrable systems with quadratic constants of motion separable in several different coordinate systems and the superintegrable systems with higher order constants of motion are analyzed

quantum integrals from coalgebra structure quantum versions of the hydrogen atom and the harmonic oscillator are studied on non euclidean spaces of dimension n integrals of arbitrary order are constructed via a multi dimensional version of the factorization method thus confirming the conjecture of riglioni 2013 j phys a math theor 46 265207 the systems are extended via coalgebra extension of representations although not all integrals are expressible in these generators as an example dimensional reduction is applied to four dimensional systems to obtain extension and new proofs of the superintegrability of known families of hamiltonians

n 2 supersymmetric extension of the tremblay turbiner winternitz hamiltonians on a plane the family of tremblay turbiner winternitz hamiltonians hk on a plane corresponding to any positive real value of k is shown to admit an supersymmetric extension of the same kind as that introduced by freedman and mende for the calogero problem and based on an superalgebra the irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion xk of hk bases for them are explicitly constructed the ground state of each supersymmetrized hamiltonian is shown to belong to an atypical lowest weight state irreducible representation

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension

superintegrable deformations of superintegrable systems quadratic superintegrability and higher order superintegrability the superintegrability of four hamiltonians hr hr r a b c d where hr are known hamiltonians and is a certain function defined on the configuration space and depended on a parameter is studied the new hamiltonians and the associated constants of motion jri i 1 2 3 are continous functions of the parameter the first part is concerned with separability and quadratic superintegrability the integrals of motion are quadratic in the momenta and the second part is devoted to the existence of higher order superintegrability the results obtained in the second part are related with the tremblay turbiner winternitz and the post winternitz systems

hamiltonians separable in cartesian coordinates and third order integrals of motion we present in this article all hamiltonian systems in e 2 that are separable in cartesian coordinates and that admit a third order integral both in quantum and in classical mechanics many of these superintegrable systems are new and it is seen that there exists a relation between quantum superintegrable potentials invariant solutions of the korteweg de vries equation and the painleve transcendents

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

nondegenerate three dimensional complex euclidean superintegrable systems and algebraic varieties a classical or quantum second order superintegrable system is an integrable n dimensional hamiltonian system with potential that admits 2n 1 functionally independent second order constants of the motion polynomial in the momenta the maximum possible such systems have remarkable properties multi integrability and multiseparability an algebra of higher order symmetries whose representation theory yields spectral information about the schrodinger operator deep connections with special functions and with quasiexactly solvable systems here we announce a complete classification of nondegenerate i e four parameter potentials for complex euclidean 3 space we characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints the euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation there are exactly ten nondegenerat

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

third order superintegrable systems separable in parabolic coordinates in this paper we investigate superintegrable systems which separate in parabolic coordinates and admit a third order integral of motion we give the corresponding determining equations and show that all such systems are multi separable and so admit two second order integrals the third order integral is their lie or poisson commutator we discuss how this situation is different from the cartesian and polar cases where new potentials were discovered which are not multi separable and which are expressed in terms of painleve transcendents or elliptic functions

cyclic concatenated codes with constacyclic outer codes the known construction of cyclic concatenated codes is based on the fact that the inner is a cyclic minimal code the outer code is cyclic and the lengths of the inner and outer codes are relatively prime it is shown that if the outer code is a suitably chosen constacyclic code the overall concatenated code is always cyclic regardless of the length of the outer code moreover it follows that any cyclic code of composite length is a direct sum of cyclic concatenated codes with inner cyclic minimal codes and outer constacyclic codes this description of cyclic codes of composite length leads to the introduction of the concept of a poor code length pcl all but low rate codes of this length have a poor minimum distance a pcl is directly related to the existence of irreducible binomials in the binary case the first few pcls are 9 25 27 45 49 75 81 and 99 arbitrarily long binary cyclic codes that are better than binary bch codes of primitive length are constructed

an infinite family of solvable and integrable quantum systems on a plane an infinite family of exactly solvable and integrable potentials on a plane is introduced it is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family the underlying algebraic structure of the new potentials is revealed as well as its hidden algebra we conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases a quasi exactly solvable and integrable generalization of the family is found

families of superintegrable hamiltonians constructed from exceptional polynomials we introduce a family of exactly solvable two dimensional hamiltonians whose wave functions are given in terms of laguerre and exceptional jacobi polynomials the hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems additional higher order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable

the concatenated structure of cyclic and abelian codes it is shown that a linear two dimensional cyclic code of length nn can be factorized into a direct sum of concatenated codes with cyclic inner and outer codes and conversely thai a two dimensional cyclic code can be constructed in this way this result is extended and it appears that the abelian codes are obtainable by taking a direct sum of several concatenations of cyclic codes codes are constructed that are better than any previously known in particular low rate cyclic codes superior to the duals of high rate bch codes are constructed

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

quasi bi hamiltonian structures complex functions and superintegrability the tremblay turbiner winternitz ttw and the post winternitz pw systems the existence of quasi bi hamiltonian structures for the tremblay turbiner winternitz ttw and the post winternitz pw systems is studied we first recall that the superintegrability of these two systems is related with the existence of certain complex functions endowed with interesting poisson bracket properties and then we prove the existence of several quasi bi hamiltonian structures making use of these complex functions this is done in two steps first with complex 2 forms wedge product of the differentials of the complex functions and then with several real 2 forms the properties of these geometric structures and the associated recursion operators are also analyzed the paper can be considered as divided in two parts in the first part a we study the ttw system related to the harmonic oscillator and in the second part we study the pw system related to the kepler problem

sharp estimates and the dirac operator this paper establishes and extends a conjecture posed by m gromov which states that every riemannian metric g on s n that strictly dominates the standard metric g 0 must have somewhere scalar curvature strictly less than that of g 0 more generally if m is any compact spin manifold of dimension n which admits a distance decreasing map f m rightarrow s n of non zero degree then either there is a point x in m with normalized scalar curvature tilde kappa x 1 or m is isometric to s n the distance decreasing hypothesis can be replaced by the weaker assumption f is contracting on 2 forms in both cases the results are sharp an explicit counterexample is given to show that the result is no longer valid if one replaces 2 forms by k forms with k geq 3

periodic orbits for an infinite family of classical superintegrable systems we show that all bounded trajectories in the two dimensional classical system with the potential are closed for all integer and rational values of k the period is and does not depend on k this agrees with our earlier conjecture suggesting that the quantum version of this system is superintegrable

concatenated codes with fixed inner code and random outer code we derive lower bounds on the distance and error exponent of the coding scheme described in the title the bounds are compared to the parameters and error performance of a concatenated code family with varying inner codes of equal rates and a fixed minimum distance separable mds code as the outer code letting the inner and outer code lengths approach infinity

generalized stackel transform and reciprocal transformations for finite dimensional integrable systems we present a multiparameter generalization of the stackel transform the latter is also known as the coupling constant metamorphosis and show that under certain conditions this generalized stackel transform preserves liouville integrability noncommutative integrability and superintegrability the corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form and we investigate the properties of this reciprocal transformation finally we show that the hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized stackel transform

families of classical subgroup separable superintegrable systems we describe a method for determining a complete set of integrals for a classical hamiltonian that separates in orthogonal subgroup coordinates as examples we use it to determine complete sets of integrals polynomial in the momenta for some families of generalized oscillator and kepler coulomb systems hence demonstrating their superintegrability the latter generalizes recent results of verrier and evans and rodriguez tempesta and winternitz another example is given of a superintegrable system on a non conformally flat space

c0 coarse geometry and scalar curvature in this paper we introduce an alternative form of coarse geometry on proper metric spaces which is more delicate at infinity than the standard metric coarse structure there is an assembly map from the k homology of a space to the k theory of the c algebra associated to the new coarse structure which factors through the coarse k homology of the space with the new coarse structure a dirac type operator on a complete riemannian manifold m gives rise to a class in k homology and its image under assembly gives a higher index in the k theory group the main result of this paper is a vanishing theorem for the index of the dirac operator on an open spin manifold for which the scalar curvature x tends to infinity as x tends to infinity this is derived from a spectral vanishing theorem for any dirac type operator with discrete spectrum and finite dimensional eigenspaces