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\(E_{2}\)-cells and mapping class groups

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Abstract

We prove a new kind of stabilisation result, “secondary homological stability,” for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of \(E_{2}\)-algebras, which have no \(E_{2}\)-cells below a certain vanishing line.

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Authors and Affiliations

  1. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen OE, Denmark

    Søren Galatius

  2. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Alexander Kupers

  3. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    Oscar Randal-Williams

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  1. Søren Galatius
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  2. Alexander Kupers
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  3. Oscar Randal-Williams
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Correspondence to Alexander Kupers.

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Galatius, S., Kupers, A. & Randal-Williams, O. \(E_{2}\)-cells and mapping class groups. Publ.math.IHES 130, 1–61 (2019). https://doi.org/10.1007/s10240-019-00107-8

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