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

Masato Mimura, Hiroki Sako

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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).

本文言語English
ページ(範囲)1-47
ページ数47
ジャーナルJournal of Topology and Analysis
13
1
DOI
出版ステータスPublished - 2021 3

ASJC Scopus subject areas

  • 分析
  • 幾何学とトポロジー

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