Costa, Armindo and Farber, Michael. (2011) Topology of random right angled Artin groups. Journal of Topology and Analysis, Vol.3 (No.1). pp. 69-87. ISSN 1793-5253

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Journal of Topology and Analysis
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	1793-5253
Date:	March 2011
Volume:	Vol.3
Number:	No.1
Page Range:	pp. 69-87
Identification Number:	10.1142/S1793525311000490
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/43438

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