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

Ferihe Atalan | Zendy; Mustafa Korkmaz | Zendy

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

Author(s) -

Ferihe Atalan,

Mustafa Korkmaz

Publication year - 2010

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-0901-38

Subject(s) - mathematics , ball (mathematics) , center (category theory) , mapping class group , pure mathematics , group (periodic table) , infinity , class (philosophy) , mathematical analysis , geometry , combinatorics , surface (topology) , crystallography , chemistry , organic chemistry , artificial intelligence , computer science

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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