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Expanders, exact crossed
products, and the Baum–Connes conjecture
Paul Baum, Erik Guentner and Rufus Willett |
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Vol. 1 (2016), No. 2, 155–208
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Abstract |
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We reformulate the Baum–Connes conjecture with coefficients by introducing a new crossed product functor for -algebras. All confirming examples for the original Baum–Connes conjecture remain confirming examples for the reformulated conjecture, and at present there are no known counterexamples to the reformulated conjecture. Moreover, some of the known expander-based counterexamples to the original Baum–Connes conjecture become confirming examples for our reformulated conjecture. |
Keywords
Gromov monster group, exotic crossed product, a-T-menable
action, girth of graph
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Mathematical Subject Classification 2010
Primary: 22D25, 46L80, 46L85, 58B34
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Milestones
Received: 14 January 2015
Revised: 21 April 2015
Accepted: 14 May 2015
Published: 20 October 2015
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Authors |
| Paul Baum | |
| Department of Mathematics The Pennsylvania State University 206 McAllister Building University Park, PA 16802 United States |
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| Erik Guentner | |
| Department of Mathematics University of Hawai‘i at Mānoa 2565 McCarthy Mall Honolulu, HI 96822-2273 United States |
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| Rufus Willett | |
| Department of Mathematics University of Hawai‘i at Mānoa 2565 McCarthy Mall Honolulu, HI 96822-2273 United States |
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