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


Atalan F., KORKMAZ M.

TURKISH JOURNAL OF MATHEMATICS, vol.34, no.4, pp.585-592, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.3906/mat-0901-38
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.585-592
  • Keywords: Mapping class group, growth series, growth functions
  • Middle East Technical University Affiliated: Yes

Abstract

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