Theti Fixed-point property of random quotients by plain words

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We show a fixed-point property of certain random groups for a wide class of CAT.0/ spaces. The model of random groups under consideration is given as the set of presentations .S;R/, where S is a generating set and the set of relations R is a subset of the set of all plain words of the same length with suitably fixed density. Our main theorem says that, with high probability, groups obtained by such presentations have the fixed-point property for all CAT.0/ spaces having bounded singularities.

元の言語English
ページ(範囲)1101-1140
ページ数40
ジャーナルGroups, Geometry, and Dynamics
8
発行部数4
DOI
出版物ステータスPublished - 2014 1 1

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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