Point pushing, homology, and the hyperelliptic involution
Geometric Topology
2011-10-10 v1 Algebraic Geometry
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. 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.
Cite
@article{arxiv.1110.1397,
title = {Point pushing, homology, and the hyperelliptic involution},
author = {Tara E. Brendle and Dan Margalit},
journal= {arXiv preprint arXiv:1110.1397},
year = {2011}
}
Comments
26 pages, 4 figures