On the homology of big mapping class groups

Abstract

We prove that the mapping class group of the one-holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once-punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite-type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite-type surfaces.

arXiv commentAccepted for publication by the Journal of Topology. 32 pages, 7 figures

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Cited by in corpus (1)

• Compact and finite-type support in the homology of big mapping class groups