JournalsggdVol. 8, No. 4pp. 1101–1140

Fixed-point property of random quotients by plain words

  • Hiroyasu Izeki

    Keio University, Yokohama, Japan
Fixed-point property of random quotients by plain words cover
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Abstract

We show a fixed-point property of certain random groups for a wide class of CAT(0) spaces. Th e model of random groups under consideration is given as the set of presentations(S,R)(S, R), where SS is a generating set and the set of relationss R is a subset of the set of all plain words of the same length with suitably xed 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.

Cite this article

Hiroyasu Izeki, Fixed-point property of random quotients by plain words. Groups Geom. Dyn. 8 (2014), no. 4, pp. 1101–1140

DOI 10.4171/GGD/257