Equivariant Callias index theory via coarse geometry

An equivariant index formula in contact geometry

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...

Equivariant KK-theory and noncommutative index theory

Coarse Geometry via Grothendieck Topologies

In the course of the last years several authors have studied index problems for open Riemannian manifolds. The abstract indices are elements in the K-theory of an associated C∗-algebra, which only depends on the ”coarse” (or large scale) geometry of the underlying metric space. In order to make these indices computable J.Roe introduced a new cohomology theory, called coarse cohomology, which is...

Genericity in Equivariant Dynamical Systems and Equivariant Fuller Index Theory

Contents Introduction 5 1 Genericity in Non-Equivariant Dynamical Systems 8 1.

Using Equivariant Obstruction Theory in Combinatorial Geometry

A significant group of problems coming from the realm of Combinatorial Geometry can only be approached through the use of Algebraic Topology. From the first such application to Kneser’s problem in 1978 by Lovász [13] through the solution of the Lovász conjecture [1], [8], many methods from Algebraic Topology have been used. Specifically, it appears that the understanding of equivariant theories...