- Turkish Journal of Mathematics
- Vol: 38 Issue: 3
- Counting pseudo-Anosov mapping classes on the 3-punctured projective plane
Counting pseudo-Anosov mapping classes on the 3-punctured projective plane
Authors : Blazej Szepietowski
Pages : 524-534
Doi:10.3906/mat-1211-7
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements.Keywords : Mapping class group, nonorientable surface, growth functions