Theti Fixed-point property of random quotients by plain words

Hiroyasu Izeki

doi:10.4171/GGD/257

Theti Fixed-point property of random quotients by plain words

Hiroyasu Izeki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1101-1140
Number of pages	40
Journal	Groups, Geometry, and Dynamics
Volume	8
Issue number	4
DOIs	https://doi.org/10.4171/GGD/257
Publication status	Published - 2014

Keywords

CAT(0) spaces
Fixed-point property
Harmonic maps
Random groups

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/257

Cite this

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abstract = "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.",

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author = "Hiroyasu Izeki",

note = "Publisher Copyright: {\textcopyright}2014 European Mathematical Society.",

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AB - 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.

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KW - Fixed-point property

KW - Harmonic maps

KW - Random groups

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Theti Fixed-point property of random quotients by plain words

Abstract

Keywords

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