Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture
Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture
We introduce a new variant of the coarse Baum–Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum–Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum–Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum–Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum–Connes conjecture in an elementary way.
306-338
Finn-Sell, Martin
af6f8f4b-ecef-4095-b410-ee0273184652
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
10 July 2014
Finn-Sell, Martin
af6f8f4b-ecef-4095-b410-ee0273184652
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Finn-Sell, Martin and Wright, Nick
(2014)
Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture.
Advances in Mathematics, 259, .
(doi:10.1016/j.aim.2014.02.029).
Abstract
We introduce a new variant of the coarse Baum–Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum–Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum–Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum–Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum–Connes conjecture in an elementary way.
Text
Spaces of Graphs Boundary Groupoids and Coarse Baum-Connes.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 26 February 2014
e-pub ahead of print date: 5 April 2014
Published date: 10 July 2014
Organisations:
Pure Mathematics
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Local EPrints ID: 369782
URI: http://eprints.soton.ac.uk/id/eprint/369782
ISSN: 0001-8708
PURE UUID: 6f33448c-e148-4d36-a3df-e158d2c6561a
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Date deposited: 13 Oct 2014 10:25
Last modified: 15 Mar 2024 03:22
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Author:
Martin Finn-Sell
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