Rank gradient and cost of Artin groups and their relatives

Journal article

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.

Authors: Kar, A; Nikolov, N

• Publication date: 2012-10-10
• Keywords: math.GR