Rank gradient and cost of Artin groups and their relatives

Author: 

Kar, A
Nikolov, N

Publication Date: 

11 February 2015

Journal: 

Groups, Geometry, and Dynamics

Last Updated: 

2020-05-13T13:16:33.487+01:00

Issue: 

4

Volume: 

8

DOI: 

10.4171/GGD/300

page: 

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.

Symplectic id: 

353977

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article