On injective homomorphisms between Teichmüller modular groups I

On injective homomorphisms between Teichmüller modular groups I

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-Hop...

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Veröffentlicht in:Inventiones mathematicae 1999, Vol.135 (2), p.425-486
Hauptverfasser: Ivanov, Nikolai V., McCarthy, John D.
Format: Artikel
Sprache:eng
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Zusammenfassung: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. [PUBLICATION ABSTRACT]
ISSN:0020-9910
1432-1297
DOI:10.1007/s002220050292