Homomorphisms from mapping class groups

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Harvey W., Korkmaz M.

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, vol.37, pp.275-284, 2005 (SCI-Expanded) identifier identifier


This paper concerns rigidity of the mapping class groups. It is shown that any homomorphism phi: Mod(g) -> Mod(h) between mapping class groups of closed orientable surfaces with distinct genera g > h is trivial if g >= 3, and has finite cyclic image for all g >= 1. Some implications are drawn for more general homomorphs of these groups.