Factoring in the hyperelliptic Torelli group

Brendle, T. E. and Margalit, D. (2015) Factoring in the hyperelliptic Torelli group. Mathematical Proceedings of the Cambridge Philosophical Society, 159(2), pp. 207-217. (doi: 10.1017/S0305004115000286)

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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. Putman and the authors proved that this group is generated by Dehn twists about separating curves fixed by the hyperelliptic involution. In this paper, we introduce an algorithmic approach to factoring a wide class of elements of the hyperelliptic Torelli group into such Dehn twists, and apply our methods to several basic types of elements. As one consequence, we answer an old question of Dennis Johnson.

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:Mathematical Proceedings of the Cambridge Philosophical Society
Publisher:Cambridge University Press
ISSN (Online):1469-8064
Published Online:19 June 2015
Copyright Holders:Copyright © 2015 Cambridge University Press
First Published:First published in Mathematical Proceedings of the Cambridge Philosophical Society 159(2):207-217
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
595131Mapping Class Groups and Related Structures.Tara BrendleEngineering & Physical Sciences Research Council (EPSRC)EP/J019593/1M&S - MATHEMATICS