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

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Atalan, Ferihe
Korkmaz, Mustafa
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Abstract
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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.
Comment: 8 pages, 1 figure
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Mathematics - Geometric Topology, 57N05, 20F38
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