The Number of Pseudo-Anosov Elements in the Mapping Class Group of a Four-Holed Sphere

Details The Number of Pseudo-Anosov Elements in the Mapping Class Group of a Four-Holed Sphere The Number of Pseudo-Anosov Elements in the Mapping Class Group of a Four-Holed Sphere

2008-04-03

arxiv.org/abs/0804.0624v1

Mathematics

Geometric Topology

8 pages, 1 figure

Scientific paper

We compute the growth series and the growth functions of reducible and
pseudo-Anosov elements of the pure mapping class group of the sphere with four
holes with respect to a certain generating set. We prove that the ratio of the
number of pseudo-Anosov elements to that of all elements in a ball with center
at the identity tends to one as the radius of the ball tends to infinity.

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