Rank gradient and cost of Artin groups and their relatives

2012/10/10 by Aditi Kar, Nikolay Nikolov, Kar, Aditi +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1210.2873

arxiv created 2014/05/02 · arxiv updated 2014/05/06

Abstract

We prove that the rank gradient vanishes for mapping class groups of genus bigger than 1, Aut(F_n), for all n, Out(F_n) for n ≥ 3, and any Artin group whose underlying graph is connected. These groups have fixed price 1. We compute the rank gradient and verify that it is equal to the first L²-Betti number for some classes of Coxeter groups.

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