Constant and Equivariant Cyclic Cohomology

Stochastic Equivariant Cohomologies and Cyclic Cohomology

We give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the Chen–Souriau sense and to establish a link with cyclic cohomology. With the second one, we can establish a stochastic fixed point theorem. 1. Introduction. Let us consider a finite-dimensional orientable mani-fold M of even dimension. Let us suppose that it is en...

Equivariant Cyclic Cohomology of Hopf Module Algebras

We introduce an equivariant version of cyclic cohomology for Hopf module algebras. For any H-module algebra A, where H is a Hopf algebra with S2 = idH we define the cocyclic module C ♮ H(A) and we find its relation with cyclic cohomology of crossed product algebra A ⋊ H. We define K 0 (A), the equivariant K-theory group of A, and its pairing with cyclic and periodic cyclic cohomology of C H(A).

Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas

For an algebra B with an action of a Hopf algebra H we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg’s theorem relating...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

The equivariant index theorem in entire cyclic cohomology

Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifoldM , with compact quotient GnM . There is an assembly map W K .M/ ! K .B/ which associates to any Gequivariant K-homology class onM , an element of the topological K-theory of a suitable Banach completion B of the convolution algebra of continuous compactly supported functions on G. The a...