Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1

arxiv: 1211.4018 · v4 · pith:57RVBJARnew · submitted 2012-11-16 · 🧮 math.GT · math.AG· math.GR

Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1

Tara Brendle , Dan Margalit , Andrew Putman This is my paper

classification 🧮 math.GT math.AGmath.GR

keywords hyperellipticgrouptorellicurvesburaukernellocusrepresentation

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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.

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Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1

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