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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. ISSN 1793-5253
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Official URL: http://dx.doi.org/10.1142/S1793525311000490
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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