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Localization for coarse homology theories

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arxiv 1902.04947 v5 pith:K27VXLWK submitted 2019-02-13 math.KT math.ATmath.MG

Ulrich Bunke , Luigi Caputi This is my paper · ORCID
classification math.KTmath.ATmath.MG
keywords coarsehomologyequivariantbredon-stylelocalizationtheoryalgebraicanalog
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abstract

We introduce the notion of a Bredon-style equivariant coarse homology theory. We show that such a Bredon-style equivariant coarse homology theory satisfies localization theorems and that a general equivariant coarse homology theory can be approximated by a Bredon-style version. We discuss the special case of algebraic and topological equivariant coarse $K$-homology and obtain the coarse analog of Segal's localization theorem.

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