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.
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Oblatum 24-III-1995 & 22-X-97 / Published online: 14 October 1998
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Ivanov, N., McCarthy, J. On injective homomorphisms between Teichmüller modular groups I. Invent math 135, 425–486 (1999). https://doi.org/10.1007/s002220050292
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DOI: https://doi.org/10.1007/s002220050292