Coarse homology theories

Coarse Geometry and K-homology

Generalized Homology Theories

Equivariant Stratifold Homology Theories

We define equivariant homology theories using bordism of stratifolds with a G-action, where G is a discrete group. Stratifolds are a generalization of smooth manifolds which were introduced by Kreck [Kre02]. He defines homology theories using bordism of suitable stratifolds. We develop the equivariant generalization of these ideas.

Controlled coarse homology and isoperimetric inequalities

We study a coarse homology theory with prescribed growth conditions. For a finitely generated group G with the word length metric this homology theory turns out to be related to amenability of G. We characterize vanishing of a certain fundamental class in our homology in terms of an isoperimetric inequality on G and show that on any group at most linear control is needed for this class to vanis...

Interpolation Categories for Homology Theories

For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture more and more information according to the injective dimension of the images of the functor. The categories are obtained by using truncated versions of resolu...