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This article is cited in 1 scientific paper (total in 1 paper)
Equivariant Coarse (Co-)Homology Theories
Christopher Wulff Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, D-37073 Göttingen, Germany
Abstract:
We present an Eilenberg–Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A large part of this paper is devoted to showing how some well-established coarse (co-)homology theories, whose equivariant versions are either already known or will be introduced in this paper, fit into this setup. Furthermore, a new and more flexible notion of coarse homotopy is given which is more in the spirit of topological homotopies. Some, but not all, coarse (co-)homology theories are even invariant under these new homotopies. They also led us to a meaningful concept of topological actions of locally compact groups on coarse spaces.
Keywords:
equivariant coarse homology, equivariant coarse cohomology, equivariant coarse assembly, equivariant coarse coassembly, generalized coarse homotopies.
Received: October 3, 2021; in final form July 15, 2022; Published online July 26, 2022
Citation:
Christopher Wulff, “Equivariant Coarse (Co-)Homology Theories”, SIGMA, 18 (2022), 057, 62 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1853 https://www.mathnet.ru/eng/sigma/v18/p57
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Abstract page: | 46 | Full-text PDF : | 18 | References: | 11 |
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