Coarse homology theories and finite decomposition complexity
Ulrich Bunke, Alexander Engel, Daniel Kasprowski, Christoph Winges
TL;DR
This paper develops an axiomatic framework using coarse homology theories to understand vanishing results related to spaces with finite decomposition complexity, focusing on fibers of forget-control maps.
Contribution
It introduces an axiomatic approach to coarse homology theories that explains vanishing phenomena in spaces with finite decomposition complexity.
Findings
Established vanishing results for fibers of forget-control maps
Provided an axiomatic account linking coarse homology to decomposition complexity
Enhanced understanding of coarse geometric invariants in complex spaces
Abstract
Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant finite decomposition complexity.
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