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arXiv · 1606.05459

Plant complexes and homological stability for Hurwitz spaces

J. Frederik Tietz
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Abstract

We study Hurwitz spaces with regard to homological stabilization. By a Hurwitz space, we mean a moduli space of branched, not necessarily connected coverings of a disk with fixed structure group and number of branch points. We choose a sequence of subspaces of Hurwitz spaces which is suitable for our investigations. In the first part, we introduce and study plant complexes, a large new class of simplicial complexes, generalizing the arc complex on a surface with marked points. In the second part, we generalize a result by Ellenberg-Venkatesh-Westerland by showing that homological stabilization of our sequence of Hurwitz spaces depends only on properties of their zeroth homology groups.

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J. Frederik Tietz. 2016-06-17. Plant complexes and homological stability for Hurwitz spaces. https://arxiv.org/abs/1606.05459

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