Brendle, T. , Margalit, D. and Putman, A. (2015) Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = -1. Inventiones Mathematicae, 200(1), pp. 263-310. (doi: 10.1007/s00222-014-0537-9)
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Abstract
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t = −1 and also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Brendle, Professor Tara |
| Authors: | Brendle, T., Margalit, D., and Putman, A. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Inventiones Mathematicae |
| Publisher: | Springer Berlin Heidelberg |
| ISSN: | 0020-9910 |
| ISSN (Online): | 1432-1297 |
| Copyright Holders: | Copyright © 2014 The Authors |
| First Published: | First published in Inventiones Mathematicae July 2014 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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