Equivariant Coarse (Co-)Homology Theories
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 wel...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2022 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211730 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Equivariant Coarse (Co-)Homology Theories. Christopher Wulff. SIGMA 18 (2022), 057, 62 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862583080591556608 |
|---|---|
| author | Wulff, Christopher |
| author_facet | Wulff, Christopher |
| citation_txt | Equivariant Coarse (Co-)Homology Theories. Christopher Wulff. SIGMA 18 (2022), 057, 62 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-13T18:18:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211730 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T18:18:05Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wulff, Christopher 2026-01-09T12:54:00Z 2022 Equivariant Coarse (Co-)Homology Theories. Christopher Wulff. SIGMA 18 (2022), 057, 62 pages 1815-0659 2020 Mathematics Subject Classification: 51F30; 5N35; 6L85 arXiv:2006.02053 https://nasplib.isofts.kiev.ua/handle/123456789/211730 https://doi.org/10.3842/SIGMA.2022.057 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. The author would like to thank Alexander Engel for insightful conversations. Furthermore, the author is also very grateful to the anonymous referees for their meticulous inspection of the manuscript, for their long list of comments, and for pointing out numerous inaccuracies. Their suggestions, critizism and partially also strong opinions had a significant positive influence on this paper. The research was supported by the DFG through the Priority Programme “Geometry at Infinity” (SPP 2026; individual project “Duality and the coarse assembly map”, WU 869/1-1, WU869/1-2). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Equivariant Coarse (Co-)Homology Theories Article published earlier |
| spellingShingle | Equivariant Coarse (Co-)Homology Theories Wulff, Christopher |
| title | Equivariant Coarse (Co-)Homology Theories |
| title_full | Equivariant Coarse (Co-)Homology Theories |
| title_fullStr | Equivariant Coarse (Co-)Homology Theories |
| title_full_unstemmed | Equivariant Coarse (Co-)Homology Theories |
| title_short | Equivariant Coarse (Co-)Homology Theories |
| title_sort | equivariant coarse (co-)homology theories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211730 |
| work_keys_str_mv | AT wulffchristopher equivariantcoarsecohomologytheories |