We prove that the rank gradient vanishes for mapping class groups of genus greater than 1, Aut(Fn) for all n, Out(Fn), 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.
Classification :
20-XX
Mots-clés :
Rank gradient, cost, Artin groups
Affiliations des auteurs :
Aditi Kar
1
;
Nikolay Nikolov
2
1
University of Southampton, UK
2
University of Oxford, UK
Aditi Kar; Nikolay Nikolov. Rank gradient and cost of Artin groups and their relatives. Groups, geometry, and dynamics, Tome 8 (2014) no. 4, pp. 1195-1205. doi: 10.4171/ggd/300
@article{10_4171_ggd_300,
author = {Aditi Kar and Nikolay Nikolov},
title = {Rank gradient and cost of {Artin} groups and their relatives},
journal = {Groups, geometry, and dynamics},
pages = {1195--1205},
year = {2014},
volume = {8},
number = {4},
doi = {10.4171/ggd/300},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/300/}
}
TY - JOUR
AU - Aditi Kar
AU - Nikolay Nikolov
TI - Rank gradient and cost of Artin groups and their relatives
JO - Groups, geometry, and dynamics
PY - 2014
SP - 1195
EP - 1205
VL - 8
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/300/
DO - 10.4171/ggd/300
ID - 10_4171_ggd_300
ER -
%0 Journal Article
%A Aditi Kar
%A Nikolay Nikolov
%T Rank gradient and cost of Artin groups and their relatives
%J Groups, geometry, and dynamics
%D 2014
%P 1195-1205
%V 8
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/300/
%R 10.4171/ggd/300
%F 10_4171_ggd_300
