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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Abstract
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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 0305-0041 |
| 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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