# Rank gradient and cost of Artin groups and their relatives

Kar, A
Nikolov, N

11 February 2015

## Journal:

Groups, Geometry, and Dynamics

## Last Updated:

2020-07-19T17:22:10.377+01:00

4

8

10.4171/GGD/300

1195-1205

## 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.

353977

Not Submitted

Journal Article