The girth alternative for mapping class groups

Details The girth alternative for mapping class groups The girth alternative for mapping class groups

2011-05-26

arxiv.org/abs/1105.5422v1

Mathematics

Group Theory

19 pages, 0 figures

Scientific paper

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.

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