Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups

Masato Mimura, Hiroki Sako

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The objective of this series is to study metric geometric properties of (coarse) disjoint unions of amenable Cayley graphs. We employ the Cayley topology and observe connections between large scale structure of metric spaces and group properties of Cayley accumulation points. In Part I, we prove that a disjoint union has property A of Yu if and only if all groups appearing as Cayley accumulation points in the space of marked groups are amenable. As an application, we construct two disjoint unions of finite special linear groups (and unimodular linear groups) with respect to two systems of generators that look similar such that one has property A and the other does not admit (fibered) coarse embeddings into any Banach space with nontrivial type (for instance, any uniformly convex Banach space).

Original languageEnglish
JournalJournal of Topology and Analysis
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • Property A
  • amenability
  • coarse embeddings
  • space of marked groups

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups'. Together they form a unique fingerprint.

Cite this