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Inventiones mathematicae

, Volume 135, Issue 2, pp 425–486 | Cite as

On injective homomorphisms between Teichmüller modular groups I

  • Nikolai V. Ivanov
  • John D. McCarthy
Article

Abstract.

In this paper and its sequel, we prove that injective homomorphisms between Teichmüller modular groups of compact orientable surfaces are necessarily isomorphisms, if an appropriately measured “size” of the surfaces in question differs by at most one. In particular, we establish the co-Hopfian property for modular groups of surfaces of positive genus.

Keywords

Orientable Surface Modular Group Positive Genus Injective Homomorphism Compact Orientable Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Nikolai V. Ivanov
    • 1
  • John D. McCarthy
    • 1
  1. 1.Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA (e-mail address: ivanov@math.msu.edu/mccarthy@math.msu.edu)US

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