Poincaré inequalities, embeddings, and wild groups

Assaf Naor, Lior Silberman

Research output: Contribution to journalArticle

45 Scopus citations

Abstract

We present geometric conditions on a metric space (Y,dY) ensuring that, almost surely, any isometric action on Y by Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov–Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s ‘wild groups’.

Original languageEnglish (US)
Pages (from-to)1546-1572
Number of pages27
JournalCompositio Mathematica
Volume147
Issue number5
DOIs
StatePublished - Sep 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Gromov’s random groups
  • Poincaré inequalities
  • fixed points

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