Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere
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.
Anahtar Kelimeler:
Mapping class group, growth series, growth functions
Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere
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.
Keywords:
Mapping class group, growth series, growth functions,
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- Casson, A..]. and Bleiler, S.A.: Automorphisms of Surfaces After Nielsen and Thurston, Cambridge University Press 1988.
- Farb, B.: Some problems on mapping class groups and moduli space in ”Problems on Mapping Class Groups and Related Topics”, ed. by B. Farb, Proc. Symp. Pure and Applied Math. 74, 11-55 2006.
- Harpe, P.: Topics in Geometric Group Theory, The University of Chicago Press, Chicago 2000.
- Ivanov, N.V.: Automorphisms of Teichmüller modular groups, Lecture Notes in Math., Springer, Berlin, 1346, 199-270 1988.
- Maher, J .: Random walks on the mapping class group, arXiv.math/0604433.
- Rivin, I.: Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphims, Duke Math.J. 142(2), 353—379 (2008).
- Takasawa, M.: Enumeration of Mapping Classes for the Torus, Geometriae Dedicata 85, 11-19 (2001).
- Ferihe ATALAN Received 27.01.2009
- Department of Mathematics, Atilim University, 06836 Ankara-TURKEY
- e—mail: fatalan©atilim.edu.tr Mustafa KORKMAZ
- Department of Mathematics,
- Middle East Technical University, 06531 Ankara-TURKEY
- e—mail: korkmaz©metu.edu.tr
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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