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Topology of random right angled Artin groups

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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. doi:10.1142/S1793525311000490

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Official URL: http://dx.doi.org/10.1142/S1793525311000490

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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
Official Date: March 2011
Dates:
DateEvent
March 2011Published
Volume: Vol.3
Number: No.1
Page Range: pp. 69-87
DOI: 10.1142/S1793525311000490
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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