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Originalsprache | Englisch |
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Seitenumfang | 34 |
Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 17 Juni 2016 |
Abstract
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2016.
Publikation: Arbeitspapier/Preprint › Preprint
}
TY - UNPB
T1 - Plant complexes and homological stability for Hurwitz spaces
AU - Tietz, Jakob Frederik
PY - 2016/6/17
Y1 - 2016/6/17
N2 - 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.
AB - 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.
M3 - Preprint
BT - Plant complexes and homological stability for Hurwitz spaces
ER -