%0 Journal Article
%T Topology of Random Right Angled Artin Groups
%A Armindo Costa
%A Michael Farber
%J Mathematics
%D 2009
%I arXiv
%X In this paper we study topological invariants of a class of random groups. Namely, we study right angled Artin groups associated to random graphs and investigate their Betti numbers, cohomological dimension and topological complexity. The latter is a numerical homotopy invariant reflecting complexity of motion planning algorithms in robotics. We show that the topological complexity of a random right angled Artin group assumes, with probability tending to one, at most three values. We use a result of Cohen and Pruidze which expresses the topological complexity of right angled Artin groups in combinatorial terms. Our proof deals with the existence of bi-cliques in random graphs.
%U http://arxiv.org/abs/0909.0887v2