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


Atalan F., KORKMAZ M.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, sa.4, ss.585-592, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 34 Konu: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0901-38
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.585-592

Özet

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