Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere

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.

Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere

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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  • Ferihe ATALAN Received 27.01.2009
  • Department of Mathematics, Atilim University, 06836 Ankara-TURKEY
  • e—mail: fatalan©atilim.edu.tr Mustafa KORKMAZ
  • Department of Mathematics,
  • Middle East Technical University, 06531 Ankara-TURKEY
  • e—mail: korkmaz©metu.edu.tr