Homomorphisms from mapping class groups

William Harvey; Mustafa Korkmaz

Homomorphisms from mapping class groups

Geometric Topology 2007-05-23 v1 Group Theory

Authors: William Harvey , Mustafa Korkmaz

Abstract

This paper concerns rigidity of the mapping class groups. We show that any homomorphism $\phi:{\rm Mod}_g\to {\rm Mod}_h$ 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.

Keywords

mapping class groups of surfaces mapping class groups torelli group

Cite

@article{arxiv.math/0307107,
  title  = {Homomorphisms from mapping class groups},
  author = {William Harvey and Mustafa Korkmaz},
  journal= {arXiv preprint arXiv:math/0307107},
  year   = {2007}
}

Comments

11 pages, 2 pictures

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