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NON-NORMAL PAIRS OF NON-EUCLIDEAN CRYSTALLOGRAPHIC GROUPS
JOSÉ LUIS ESTÉVEZ, MILAGROS IZQUIERDO
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 1 / February 2006

Published online by Cambridge University Press:

30 January 2006, pp. 113-123

Print publication:

February 2006
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Let $\Gamma$ be a non-Euclidean crystallographic group. $\Gamma$ is said to be non-maximal if there exists a non-Euclidean crystallographic group $\Gamma'$ such that $\Gamma \le \Gamma'$ and the dimension of the Teichmüller space of $\Gamma$ equals the dimension of the Teichmüller space of $\Gamma'$. The full list of such pairs of groups is computed in the case when $\Gamma$ is non-normal in $\Gamma'$. The corresponding problem for Fuchsian groups was solved by Singerman.

HOMOMORPHISMS FROM MAPPING CLASS GROUPS
WILLIAM J HARVEY, MUSTAFA KORKMAZ
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 2 / March 2005

Published online by Cambridge University Press:

10 March 2005, pp. 275-284

Print publication:

March 2005
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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.