The girth alternative for mapping class groups
Group Theory
2011-05-30 v1 Geometric Topology
Abstract
The girth of a finitely generated group G is the supremum of the girth of Cayley graphs for G over all finite generating sets. Let G be a finitely generated subgroup of the mapping class group Mod(S), where S is a compact orientable surface. Then, either G is virtually abelian or it has infinite girth; moreover, if we assume that G is not infinite cyclic, these alternatives are mutually exclusive.
Cite
@article{arxiv.1105.5422,
title = {The girth alternative for mapping class groups},
author = {Kei Nakamura},
journal= {arXiv preprint arXiv:1105.5422},
year = {2011}
}
Comments
19 pages, 0 figures