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

Date

2010-01-01

Author

Atalan, Ferihe
Korkmaz, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

163
views

0
downloads

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

Subject Keywords

Mapping class group, Growth series, Growth functions

URI

https://hdl.handle.net/11511/39700

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-0901-38

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Prime graphs of solvable groups Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8) If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
Torsion Generators Of The Twist Subgroup Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01) We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.
Automorphisms of curve complexes on nonorientable surfaces Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01) For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
Finite rigid sets in curve complexes of non-orientable surfaces Ilbıra, Sabahattin; Korkmaz, Mustafa; Department of Mathematics (2017) A finite rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map defined on this subcomplex into the curve complex is induced from an automorphism of curve complex. In this thesisi we find finite rigid sets in the curve complexes of connected, non-orientable surfaces of genus g with n holes, where g+n neq 4.
Bohr radii of elliptic regions Kaptanoglu, HT; Sadik, N (2005-07-01) We use Faber series to define the Bohr radius for a simply connected planar domain bounded by an analytic Jordan curve. We estimate the value of the Bohr radius for elliptic domains of small eccentricity and show that these domains do not exhibit Bohr phenomenon when the eccentricity is large. We obtain the classical Bohr radius as the eccentricity tends to 0.

Citation Formats

F. Atalan and M. Korkmaz, “Number of pseudo-Anosov elements in the mapping class group of a four-holed sphere,” TURKISH JOURNAL OF MATHEMATICS, pp. 585–592, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39700.