Homomorphisms from mapping class groups

William Harvey; Mustafa Korkmaz

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Homomorphisms from mapping class groups

William Harvey·Mustafa Korkmaz

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Abstract

This paper concerns rigidity of the mapping class groups. We show that any homomorphism $ϕ:{\rm Mod}_g\to {\rm Mod}_h$ between mapping class groups of closed orientable surfaces with distinct genera $g>h$ is trivial if $g\geq 3$ and has finite image for all $g\geq 1$. Some implications are drawn for more general homomorphs of these groups.

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BibTeX RIS

William Harvey, Mustafa Korkmaz. 2003-07-09. Homomorphisms from mapping class groups. https://arxiv.org/abs/math/0307107

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