### 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 | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

**Theti Fixed-point property of random quotients by plain words.** / Izeki, Hiroyasu.

Research output: Contribution to journal › Article

*Groups, Geometry, and Dynamics*, vol. 8, no. 4, pp. 1101-1140. https://doi.org/10.4171/GGD/257

}

TY - JOUR

T1 - Theti Fixed-point property of random quotients by plain words

AU - Izeki, Hiroyasu

PY - 2014

Y1 - 2014

N2 - 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.

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.

KW - CAT(0) spaces

KW - Fixed-point property

KW - Harmonic maps

KW - Random groups

UR - http://www.scopus.com/inward/record.url?scp=84923585104&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923585104&partnerID=8YFLogxK

U2 - 10.4171/GGD/257

DO - 10.4171/GGD/257

M3 - Article

AN - SCOPUS:84923585104

VL - 8

SP - 1101

EP - 1140

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

SN - 1661-7207

IS - 4

ER -