Martin David Palmer -- Preprint -- On the homology of big mapping class groups
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On the homology of big mapping class groups
with Xiaolei Wu
(v1: 2022)

arXiv: abspdf
v1

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.

Here are the notes of a talk that I gave, based on the results of this paper, on 21 November 2022 at the Moduli and Friends seminar.