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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
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: |
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| 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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