Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1
| dc.citation.firstpage | 263 | |
| dc.citation.issueNumber | 1 | |
| dc.citation.journalTitle | Inventiones mathematicae | |
| dc.citation.lastpage | 310 | |
| dc.citation.volumeNumber | 200 | |
| dc.citation.volumeNumber | en_US | |
| dc.contributor.author | Brendle, Tara | |
| dc.contributor.author | Margalit, Dan | |
| dc.contributor.author | Putman, Andrew | |
| dc.date.accessioned | 2017-05-15T17:23:58Z | |
| dc.date.available | 2017-05-15T17:23:58Z | |
| dc.date.issued | 2015 | |
| dc.description.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. | |
| dc.identifier.citation | Brendle, Tara, Margalit, Dan and Putman, Andrew. "Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1." <i>Inventiones mathematicae,</i> 200, no. 1 (2015) Springer: 263-310. http://dx.doi.org/10.1007/s00222-014-0537-9. | |
| dc.identifier.doi | http://dx.doi.org/10.1007/s00222-014-0537-9 | |
| dc.identifier.uri | https://hdl.handle.net/1911/94256 | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.rights | This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/us/ | |
| dc.title | Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1 | |
| dc.type | Journal article | |
| dc.type.dcmi | Text | |
| dc.type.publication | publisher version |
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