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Big Torelli groups: generation and commensuration. (arXiv:1810.03453v1 [math.GT])
来源于:arXiv
For any surface $\Sigma$ of infinite topological type, we study the Torelli
subgroup $\mathcal{I}(\Sigma)$ of the mapping class group ${\rm Mod}(\Sigma)$,
whose elements are those mapping classes that act trivially on the homology of
$\Sigma$. Our first result asserts that $\mathcal{I}(\Sigma)$ is topologically
generated by the subgroup of ${\rm Mod}(\Sigma)$ consisting of those elements
which have compact support. In particular, using results of Birman and Powell,
we deduce that $\mathcal{I}(\Sigma)$ is topologically generated by {\em
separating twists} and {\em bounding pair maps}. Next, we prove that the
abstract commensurator of $\mathcal{I}(\Sigma)$ coincides with ${\rm
Mod}(\Sigma)$. This extends results of Farb-Ivanov and Kida to the setting of
infinite--type surfaces. 查看全文>>