Asymptotics for pseudo-Anosov elements in Teichmuller lattices

Details Asymptotics for pseudo-Anosov elements in Teichmuller lattices Asymptotics for pseudo-Anosov elements in Teichmuller lattices

2009-01-18

arxiv.org/abs/0901.2679v2

Mathematics

Geometric Topology

17 pages, 2 figures, revised version.

Scientific paper

A Teichmuller lattice is the orbit of a point in Teichmuller space under the action of the mapping class group. We show that the proportion of lattice points in a ball of radius r which are not pseudo-Anosov tends to zero as r tends to infinity. In fact, we show that if R is a subset of the mapping class group, whose elements have an upper bound on their translation length on the complex of curves, then proportion of lattice points in the ball of radius r which lie in R tends to zero as r tends to infinity.

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