Topology of random right angled Artin groups
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 1793-5253Full text not available from this repository.
Official URL: http://dx.doi.org/10.1142/S1793525311000490
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.|
|Page Range:||pp. 69-87|
|Access rights to Published version:||Restricted or Subscription Access|
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