Open AccessThe girth alternative for mapping class groups
Author(s) -
Kei Nakamura
Publication year - 2014
Publication title -
groups geometry and dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.05
H-Index - 25
eISSN - 1661-7215
pISSN - 1661-7207
DOI - 10.4171/ggd/223
Subject(s) - mathematics , girth (graph theory) , class (philosophy) , combinatorics , discrete mathematics , algebra over a field , pure mathematics , computer science , artificial intelligence
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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