Ulrich Bunke: A universal equivariant coarse K-homology

Coffee: 14:30-15:00
Abstract: In analogy to \(A^1\)-homotopy theory I will introduce a universal equivariant coarse homology theory. As an example, I describe the construction of a universal equivariant coarse homology theory with values in the stable infinity category which was introduced by Blumberg-Gepner-Tabuada in order to capture the universal properties of the algebraic K-theory functor. From this universal theory one can derive the usual equivariant coarse K-homology, but also also other coarse homology theories like versions of THH and natural transformations between them.

Finally I will explain the relation of the coarse constructions with equivariant homology theories in the sense of Davis-Lück, and how assembly are arrise from coarse constructions.