Turkish Journal of Mathematics
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.
DOI
10.3906/mat-0901-38
Keywords
Mapping class group, growth series, growth functions
First Page
585
Last Page
592
Recommended Citation
ATALAN, F, & KORKMAZ, M (2010). Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere. Turkish Journal of Mathematics 34 (4): 585-592. https://doi.org/10.3906/mat-0901-38
