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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 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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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