Factoring in the hyperelliptic Torelli group

Details Factoring in the hyperelliptic Torelli group Factoring in the hyperelliptic Torelli group

2012-02-10

arxiv.org/abs/1202.2365v1

Mathematics

Geometric Topology

21 pages, 17 figures

Scientific paper

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. Hain conjectured that this group is generated by Dehn twists about symmetric separating curves, that is, separating curves fixed by the hyperelliptic involution. We describe two basic types of elements of the hyperelliptic Torelli group, and give explicit factorizations into Dehn twists about symmetric separating curves. Our factorizations correspond to new, intricate relations in the pure braid group.

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