The coarse Baum-Connes conjecture via Co coarse geometry
The coarse Baum-Connes conjecture via Co coarse geometry
The C0 coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C0 version of the coarse Baum–Connes conjecture and show that K*(C*X0) is a topological invariant for a broad class of metric spaces. Using this result we construct a ‘geometric’ obstruction group to the coarse Baum–Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum–Connes conjecture in this context.
coarse geometry, novikov conjecture, baum–connes conjecture, non-commutative geometry
265-303
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
2005
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Wright, Nick
(2005)
The coarse Baum-Connes conjecture via Co coarse geometry.
Journal of Functional Analysis, 220 (2), .
(doi:10.1016/j.jfa.2004.02.016).
Abstract
The C0 coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C0 version of the coarse Baum–Connes conjecture and show that K*(C*X0) is a topological invariant for a broad class of metric spaces. Using this result we construct a ‘geometric’ obstruction group to the coarse Baum–Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum–Connes conjecture in this context.
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Published date: 2005
Keywords:
coarse geometry, novikov conjecture, baum–connes conjecture, non-commutative geometry
Identifiers
Local EPrints ID: 29902
URI: http://eprints.soton.ac.uk/id/eprint/29902
ISSN: 0022-1236
PURE UUID: b4cf02da-c458-43a4-8787-311f62c12785
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Date deposited: 15 May 2006
Last modified: 16 Mar 2024 03:43
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