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  Equivariant coarse homotopy theory and coarse algebraic K-homology

Bunke, U., Engel, A., Kasprowski, D., & Winges, C. (2020). Equivariant coarse homotopy theory and coarse algebraic K-homology. In G. Cortiñas, & C. A. Weibel (Eds.), K-theory in algebra, analysis and topology: ICM 2018 Satellite School and Workshop K-theory Conference, Argentina, 2018, July 16-20 and July 23-27, 2018 La Plata and Buenos Aires, Argentina (pp. 13-104). Providence, RI: American Mathematical Society.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-CC8D-6 Version Permalink: https://hdl.handle.net/21.11116/0000-0006-E663-7
Genre: Conference Paper
Latex : Equivariant coarse homotopy theory and coarse algebraic $\boldsymbol{K}$-homology

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https://doi.org/10.1090.conm/749 (Publisher version)
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 Creators:
Bunke, Ulrich, Author
Engel, Alexander, Author
Kasprowski, Daniel1, Author           
Winges, Christoph1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, K-Theory and Homology, Metric Geometry
 Abstract: We study equivariant coarse homology theories through an axiomatic framework.
To this end we introduce the category of equivariant bornological coarse spaces
and construct the universal equivariant coarse homology theory with values in
the category of equivariant coarse motivic spectra. As examples of equivariant
coarse homology theories we discuss equivariant coarse ordinary homology and
equivariant coarse algebraic $K$-homology. Moreover, we discuss the cone
functor, its relation with equivariant homology theories in equivariant
topology, and assembly and forget-control maps. This is a preparation for
applications in subsequent papers aiming at split-injectivity results for the
Farrell-Jones assembly map.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1710.04935
URI: http://arxiv.org/abs/1710.04935
DOI: 10.1090.conm/749/15068
 Degree: -

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Title: ICM 2018 Satellite Workshop K-theory Conference
Place of Event: Buenos Aires
Start-/End Date: 2018-07-23 - 2018-07-27

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Title: K-theory in algebra, analysis and topology : ICM 2018 Satellite School and Workshop K-theory Conference, Argentina, 2018, July 16-20 and July 23-27, 2018 La Plata and Buenos Aires, Argentina
Source Genre: Proceedings
 Creator(s):
Cortiñas, Guillermo , Editor
Weibel, Charles A., Editor
Affiliations:
-
Publ. Info: Providence, RI : American Mathematical Society
Pages: vii, 388 Volume / Issue: - Sequence Number: - Start / End Page: 13 - 104 Identifier: ISBN: 978-1-4704-5026-7
DOI: 10.1090.conm/749

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Title: Contemporary mathematics
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 749 Sequence Number: - Start / End Page: - Identifier: -