Transfers in coarse homology
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 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.
353-424
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Engel, Alexander
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Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
24 August 2020
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Engel, Alexander
fc6fd4f0-2233-498a-8292-d32b7a082aa5
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
Bunke, Ulrich, Engel, Alexander, Kasprowski, Daniel and Winges, Christoph
(2020)
Transfers in coarse homology.
Munster Journal of Mathematics, 13, .
Abstract
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.
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Accepted/In Press date: 19 December 2019
Published date: 24 August 2020
Identifiers
Local EPrints ID: 478547
URI: http://eprints.soton.ac.uk/id/eprint/478547
ISSN: 1867-5778
PURE UUID: 591d16d6-318e-4e72-9b79-13992c523d71
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Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19
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Contributors
Author:
Ulrich Bunke
Author:
Alexander Engel
Author:
Daniel Kasprowski
Author:
Christoph Winges
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