Vol. 1, No. 2, 2016

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Expanders, exact crossed products, and the Baum–Connes conjecture

Paul Baum, Erik Guentner and Rufus Willett

Vol. 1 (2016), No. 2, 155–208
Abstract

We reformulate the Baum–Connes conjecture with coefficients by introducing a new crossed product functor for C-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
Mathematical Subject Classification 2010
Primary: 22D25, 46L80, 46L85, 58B34
Milestones
Received: 14 January 2015
Revised: 21 April 2015
Accepted: 14 May 2015
Published: 20 October 2015
Authors
Paul Baum
Department of Mathematics
The Pennsylvania State University
206 McAllister Building
University Park, PA 16802
United States
Erik Guentner
Department of Mathematics
University of Hawai‘i at Mānoa
2565 McCarthy Mall
Honolulu, HI 96822-2273
United States
Rufus Willett
Department of Mathematics
University of Hawai‘i at Mānoa
2565 McCarthy Mall
Honolulu, HI 96822-2273
United States