Prof. Dr. Ulrich Bunke (10.30 - 11.30)

A unified approach to coarse K-homology

Abstract: I will sketch a unified approach to equivariant coarse K-homology
theories. It takes as  input   a co-Waldhausen infinity category C in the sense of Barwick. I will discuss the definition of the  co-Waldhausen infinity category of equivariant objects in C controlled by a bornological coarse space with a group action. The basic properties of this construction are coarse invariance, preservation of flasques, u-continuity and excision. Equivariant coarse K-homology is  then defined by post-composition with suitable K-theory-like functors. In special cases our construction reproduces the classical coarse K-homology functors.