A recipe for short-word pseudo-Anosovs

By Johanna Mangahas. 2010

51 citations recorded by the source corpus.

Given any generating set of any subgroup $G$ of the mapping class group of a surface, we find an element $f$ with word length bounded by a constant $K$ depending only on the surface, and with the property that the minimal subsurface supporting a power of $f$ is as large as possible for elements of $G$. In particular, if $G$ contains a pseudo-Anosov map, we find one of word length at most $K$. We also find new examples of convex cocompact free subgroups of the mapping class group.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aed79a1873ba3d262a1f4735ccc5e2e57d132398

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Citations in the corpus

Embedability between right-angled Artin groups (2011, background): “For (iii), apply [24] to ψ −k 1 ψ m n .”
Boundaries and automorphisms of hierarchically hyperbolic spaces (2016, background): “nibus Subgroup Theorem for mapping class groups, due to HandelMosher [HM10], which they proved as an umbrella theorem for several subgroup structure theorems, including the Tits alternative; see also [Man13] for further discussion. We also obtain a coarse/HHS version of the rank-rigidity conjecture ”