Fixed-point property of random groups

Hiroyasu Izeki, Takefumi Kondo, Shin Nayatani

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, using the generalized version of the theory of combinatorial harmonic maps, we give a criterion for a finitely generated group Γ to have the fixed-point property for a certain class of Hadamard spaces, and prove a fixed-point theorem for random-group actions on the same class of Hadamard spaces. We also study the existence of an equivariant energy-minimizing map from a Γ-space to the limit space of a sequence of Hadamard spaces with the isometric actions of a finitely generated group Γ. As an application, we present the existence of a constant which may be regarded as a Kazhdan constant for isometric discrete-group actions on a family of Hadamard spaces.

Original languageEnglish
Pages (from-to)363-379
Number of pages17
JournalAnnals of Global Analysis and Geometry
Volume35
Issue number4
DOIs
Publication statusPublished - 2009 Jun 1

Keywords

  • Finitely generated group
  • Fixed-point property
  • Hadamard space
  • Harmonic map
  • Random group
  • Rigidity

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology

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