Transfers in coarse homology
We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic K-homology and equivariant coarse ordinary homology can be extended to equivariant coars...
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| Further contributors: | |
| Division/Institute: | FB 10: Mathematik und Informatik |
| Document types: | Article |
| Media types: | Text |
| Publication date: | 2020 |
| Date of publication on miami: | 24.08.2020 |
| Modification date: | 05.01.2021 |
| Source: | Münster Journal of Mathematics, 13 (2020), S. 353-424 |
| Publisher: |
Mathematisches Institut (Universität Münster)
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| Edition statement: | [Electronic ed.] |
| DDC Subject: | 510: Mathematik |
| License: | InC 1.0 |
| Language: | English |
| Format: | PDF document |
| URN: | urn:nbn:de:hbz:6-90169657484 |
| Other Identifiers: | DOI: 10.17879/90169656968 |
| Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-90169657484 |
| Digital documents: | mjm_2020_13_353-424.pdf |
We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic K-homology and equivariant coarse ordinary homology can be extended to equivariant coarse homology theories with transfers. In the case of a finite group, we observe that equivariant coarse homology theories with transfers provide Mackey functors. We express standard constructions with Mackey functors in terms of coarse geometry, and we demonstrate the usage of transfers in order to prove injectivity results about assembly maps.