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On the Baum-Connes conjecture for groups acting on CAT(0)-cubical spaces

On the Baum-Connes conjecture for groups acting on CAT(0)-cubical spaces
On the Baum-Connes conjecture for groups acting on CAT(0)-cubical spaces
We give a new proof of the Baum–Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the Julg–Valette complex of a CAT(0)-cubical space introduced by the 1st three authors and the direct splitting method in Kasparov theory developed by the last author.
1687-0247
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Guentner, Erik
0efa2b74-da7d-497d-8a80-e668eb8f41f1
Higson, Nigel
fdac8f8c-825f-482c-9ea1-b97e956a2b24
Nishikawa, Shintaro
182ea96f-577a-45b4-97dd-849670519dfe
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Guentner, Erik
0efa2b74-da7d-497d-8a80-e668eb8f41f1
Higson, Nigel
fdac8f8c-825f-482c-9ea1-b97e956a2b24
Nishikawa, Shintaro
182ea96f-577a-45b4-97dd-849670519dfe

Brodzki, Jacek, Guentner, Erik, Higson, Nigel and Nishikawa, Shintaro (2020) On the Baum-Connes conjecture for groups acting on CAT(0)-cubical spaces. International Mathematics Research Notices, 0, [rnaa059]. (doi:10.1093/imrn/rnaa059).

Record type: Article

Abstract

We give a new proof of the Baum–Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the Julg–Valette complex of a CAT(0)-cubical space introduced by the 1st three authors and the direct splitting method in Kasparov theory developed by the last author.

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Accepted/In Press date: 13 March 2020
e-pub ahead of print date: 17 April 2020
Published date: 17 April 2020
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Identifiers

Local EPrints ID: 439712
URI: http://eprints.soton.ac.uk/id/eprint/439712
DOI: doi:10.1093/imrn/rnaa059
ISSN: 1687-0247
PURE UUID: 215cbac7-f22e-4571-82e7-08ba6a5b2ce2
ORCID for Jacek Brodzki: ORCID iD orcid.org/0000-0002-4524-1081

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Date deposited: 30 Apr 2020 16:30
Last modified: 17 Mar 2024 02:54

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Author: Jacek Brodzki ORCID iD
Author: Erik Guentner
Author: Nigel Higson
Author: Shintaro Nishikawa

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