The equivariant coarse index is well-understood and widely used for actions by discrete groups. We first extend the definition of this to general locally compact use a suitable notion admissible modules over C * -algebras continuous functions obtain meaningful index. Inspired work Roe, we then develop localised variant, with values in K-theory group -algebra. This generalises Baum–Connes assemb...

In this paper we consider a class of connected closed G-manifolds with a non-empty finite fixed point set, each M of which is totally non-homologous to zero in MG (or G-equivariantly formal), where G = Z2. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a G-manifold in terms of algebra, so that we can obtain analytic descriptions of ...

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a factorisation. These factorisations are models for the topological index map....

A strange attractor (SA) with symmetry group G can be mapped down to an image strange attractor SA without symmetry by a smooth mapping with singularities. The image SA can be lifted to many distinct structurally stable strange attractors, each equivariant under G, all with the same image SA. If the symbolic dynamics of the image SA requires s symbols sigma(1),sigma(2), em leader,sigma(s), then...

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular,...

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of [5] is related to the equivariant index of [1, 6] for an associated transversally elliptic operator.

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalized coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of [4] is related to the equivariant index of [1, 5] for an associated transversally elliptic operator.