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Topology of random right angled Artin groups

By Armindo Costa and Michael Farber

Abstract

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, when n → ∞. 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

Topics: QA
Publisher: World Scientific Publishing Co. Pte. Ltd.
Year: 2011
DOI identifier: 10.1142/s1793525311000490
OAI identifier: oai:wrap.warwick.ac.uk:43438
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