Skip to main content
SpringerLink
Log in

Enumeration of Mapping Classes for the Torus

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We enumerate periodic, reducible, and Anosov elements of the mapping class group of the torus, and determine their growth function. Then we prove that almost all elements of the mapping class group of the torus are Anosov.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Birman, J. S.: Braids, Links, and Mapping Class Groups, Princeton Univ. Press, 1975.

  2. Brady, T.: Automorphism groups of punctured surfaces, Topology Appl. 55 (1994) 47–66.

    Google Scholar 

  3. Cannon, J. W.: Colored graphs, preprint.

  4. Casson, A. J. and Bleiler, S. A.: Automorphisms of Surfaces after Nielsen and Thurston, Cambridge Univ. Press, 1988.

  5. Lyndon, R. C. and Schupp, P. E.: Combinatorial Group Theory, Springer-Verlag, New York, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama 2-12-1, Meguro-ku, Tokyo, 152-8552, Japan

    M. Takasawa

Authors
  1. M. Takasawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takasawa, M. Enumeration of Mapping Classes for the Torus. Geometriae Dedicata 85, 11–19 (2001). https://doi.org/10.1023/A:1010324019197

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010324019197

Search

Navigation