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HOMOMORPHISMS FROM MAPPING CLASS GROUPS

Published online by Cambridge University Press:  10 March 2005

WILLIAM J HARVEY  and
MUSTAFA KORKMAZ
WILLIAM J HARVEY
Affiliation:
Department of Mathematics, King's College, London WC2R 2LS, United Kingdombill.harvey@kcl.ac.uk
MUSTAFA KORKMAZ
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkeykorkmaz@arf.math.metu.edu.tr
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Abstract

This paper concerns rigidity of the mapping class groups. It is shown that any homomorphism $\varphi\,{:}\,\mcg_g\,{\to}\,\mcg_h$ between mapping class groups of closed orientable surfaces with distinct genera $g\,{>}\,h$ is trivial if $g\,{\geq}\, 3$, and has finite cyclic image for all $g\,{\geq}\, 1$.

Some implications are drawn for more general homomorphs of these groups.

Keywords

57N05 (primary)20E2530F10 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 275 - 284
Copyright
© The London Mathematical Society 2005

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