共查询到20条相似文献,搜索用时 15 毫秒
1.
We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. Our construction uses no special features of equivariant K-theory. To highlight this, we construct bivariant extensions for arbitrary equivariant multiplicative cohomology theories.We formulate necessary and sufficient conditions for certain duality isomorphisms in the topological bivariant K-theory and verify these conditions in some cases, including smooth manifolds with a smooth cocompact action of a Lie group. One of these duality isomorphisms reduces bivariant K-theory to K-theory with support conditions. Since similar duality isomorphisms exist in Kasparov theory, the topological and analytic bivariant K-theories agree if there is such a duality isomorphism. 相似文献
2.
Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of
Lefschetz numbers for self-maps to an equivariant K-homology class. We compute the Lefschetz invariants for self-maps of finite-dimensional
simplicial complexes and smooth manifolds. The resulting invariants are independent of the extra structure used to compute
them. Since smooth manifolds can be triangulated, we get two formulas for the same Lefschetz invariant in this case. The resulting
identity is closely related to the equivariant Lefschetz Fixed Point Theorem of Lück and Rosenberg. 相似文献
3.
Richard Zekri 《K-Theory》1992,6(4):335-346
We consider smooth dynamical systems with unital algebra. We show that the corresponding crossed product isH-unital, and use differentiable Thom elements for proving a Thom isomorphism in bivariant periodic cohomology. 相似文献
4.
Mark Lichtner Mindaugas Radziunas Lutz Recke 《Mathematical Methods in the Applied Sciences》2007,30(8):931-960
We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
5.
The existence of bivariant Chern classes was conjectured by W. Fulton and R. MacPherson and proved by J.-P. Brasselet for cellular morphisms of analytic varieties. However, its uniqueness has been unsolved since then. In this paper we show that restricted to morphisms whose target varieties are possibly singular but (rational) homology manifolds (such as orbifolds), the bivariant Chern classes (with rational coefficients) are uniquely determined. We also discuss some related results and problems. 相似文献
6.
Richard Bödi 《Geometriae Dedicata》1998,72(3):283-297
Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such that the geometric operations of join and intersection are smooth. A systematic study of such planes and of their collineation groups can be found in previous works of the author. We prove in this paper that a 16-dimensional smooth projective plane which admits a collineation group of dimension d 39 is isomorphic to the octonion projective plane P2 O. For topological compact projective planes this is true if d 41. Note that there are nonclassical topological planes with a collineation group of dimension 40. 相似文献
7.
We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function.
A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.
8.
In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori. 相似文献
9.
In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds. 相似文献
10.
A. V. Romanov 《Mathematical Notes》2000,68(3):378-385
An example of a dissipative semilinear parabolic equation in a Hilbert space without smooth inertial manifolds is constructed.
Moreover, the attractor of this equation can be embedded in no finite-dimensionalC
1 invariant submanifold of the phase space. The class of scalar reaction-diffusion equations in bounded domains Ω ⊂ ℝm without inertial manifolds
with the property of absolute normal hyperbolicity on the setE of stationary points of the phase semiflow is described. Such equations may have inertial manifolds with the weaker property
of normal hyperbolicity onE. Three-dimensional reaction-diffusion systems without inertial manifolds normally hyperbolic at stationary points are found.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 439–447, September, 2000. 相似文献
11.
We prove that smooth maps are dense in the sense of biting convergence in W
1, 1(M, N) when M and Nare compact Riemannian manifolds and N is closed. 相似文献
12.
Atabey Kaygun 《代数通讯》2013,41(7):2513-2537
For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension of Connes' cyclic category Λ. We show that, in the case of module coalgebras, bivariant Hopf cyclic cohomology specializes to Hopf cyclic cohomology of Connes and Moscovici and its dual version by fixing either one of the variables as the ground field. We also prove an appropriate version of Morita invariance for both of these theories. 相似文献
13.
In this paper we construct a bivariant version of cyclic cohomology and study its fundamental properties. We prove universal coefficient theorems relating the bivariant theory with cyclic homology and cohomology, we construct products in the bivariant theory, and we analyse the notion of an HC-equivalence.Dedicated to Alexander Grothendieck 相似文献
14.
Isaac Pesenson 《Journal of Geometric Analysis》2009,19(2):390-419
An approximation theory by bandlimited functions (≡ Paley-Wiener functions) on Riemannian manifolds of bounded geometry is
developed. Based on this theory multiscale approximations to smooth functions in Sobolev and Besov spaces on manifolds are
obtained. The results have immediate applications to the filtering, denoising and approximation and compression of functions
on manifolds. There exists applications to problems arising in data dimension reduction, image processing, computer graphics,
visualization and learning theory.
相似文献
15.
Banach流形上映射度 总被引:1,自引:0,他引:1
本文讨论一种无限维流形上拓扑不变量,即具有可定向Fredholm结构的实Banach流形上 Cr 映射度.它是通常有限维流形上光滑映射度的一种自然推广. 相似文献
16.
Richard McGehee Evelyn Sander 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(4):497-513
We give a new proof of the stable manifold theorem for hyperbolic fixed points of smooth maps. This proof shows that the local stable and unstable manifolds are projections of a relation obtained as a limit of the graphs of the iterates of the map. The same proof generalizes to the setting of stable and unstable manifolds for smooth relations. 相似文献
17.
Anand DESSAI 《Frontiers of Mathematics in China》2016,11(5):1151-1187
We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry. 相似文献
18.
We consider translators on manifolds with singularities of the type of a transversal intersection of smooth manifolds. We give the definition of ellipticity of translators, prove the finiteness (Fredholm property) theorem, and establish an index formula for the case of point singularities. 相似文献
19.
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
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Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root. 相似文献
20.
Karl-Hermann Neeb 《Monatshefte für Mathematik》1991,112(4):303-321