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We study Hurwitz spaces with regard to homological stabilization. By aHurwitz space, we mean a moduli space of branched, not necessarily connectedcoverings of a disk with fixed structure group and number of branch points. Wechoose a sequence of subspaces of Hurwitz spaces which is suitable for ourinvestigations.  In the first part, we introduce and study plant complexes, a large new classof simplicial complexes, generalizing the arc complex on a surface with markedpoints. In the second part, we generalize a result byEllenberg-Venkatesh-Westerland by showing that homological stabilization of oursequence of Hurwitz spaces depends only on properties of their zeroth homologygroups.

Plant complexes and homological stability for Hurwitz spaces