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arXiv · 1210.2873

Rank gradient and cost of Artin groups and their relatives

Aditi Kar·Nikolay Nikolov
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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 $n \geq 3$, 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 $L^2$-Betti number for some classes of Coxeter groups.

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Aditi Kar, Nikolay Nikolov. 2014-05-02. Rank gradient and cost of Artin groups and their relatives. https://arxiv.org/abs/1210.2873

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