Point pushing, homology, and the hyperelliptic involution

Brendle, T.E. and Margalit, D. (2013) Point pushing, homology, and the hyperelliptic involution. Michigan Mathematical Journal, 62(3), pp. 451-473. (doi: 10.1307/mmj/1378757883)

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The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. We prove a Birman exact sequence for hyperelliptic Torelli groups, and we show that this sequence splits. As a consequence, we show that the hyperelliptic Torelli group is generated by Dehn twists if and only if it is generated by reducible elements. We also give an application to the kernel of the Burau representation.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Brendle, Professor Tara
Authors: Brendle, T.E., and Margalit, D.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Michigan Mathematical Journal
ISSN (Online):1945-2365
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