English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, the first of a series of two, we continue the study of higherindex theory for expanders. We prove that if a sequence of graphs is anexpander and the girth of the graphs tends to infinity, then the coarseBaum-Connes assembly map is injective, but not surjective, for the associatedmetric space $X$.  Expanders with this girth property are a necessary ingredient in theconstruction of the so-called `Gromov monster' groups that (coarsely) containexpanders in their Cayley graphs. We use this connection to show that theBaum-Connes assembly map with certain coefficients is injective but notsurjective for these groups. Using the results of the second paper in thisseries, we also show that the maximal Baum-Cones assembly map with thesecoefficients is an isomorphism.

Higher index theory for certain expanders and Gromov monster groups I