English

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.

Keywords

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

R2 v1 2026-06-21T18:13:20.833Z