Higher index theory for certain expanders and Gromov monster groups, II Academic Article

abstract

• In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an isomorphism for the associated metric space X. As discussed in the first paper in this series, this has applications to the Baum-Connes conjecture for 'Gromov monster' groups.We also introduce a new property, 'geometric property (T)'. For the metric space associated to a sequence of graphs, this property is an obstruction to the maximal coarse assembly map being an isomorphism. This enables us to distinguish between expanders with girth tending to infinity, and, for example, those constructed from property (T) groups. 2011 Elsevier Inc.

authors

• Yu, Guoliang

published proceedings

• Advances in Mathematics

author list (cited authors)

• Willett, R., & Yu, G.

citation count

• 23

complete list of authors

• Willett, Rufus||Yu, Guoliang

publication date

• January 2012

publisher

• Elsevier  Publisher

published in

• Advances in Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1016/j.aim.2011.12.016

start page

• 1762

end page

• 1803

volume

• 229

issue

• 3

URL

• http://dx.doi.org/10.1016/j.aim.2011.12.016