Publications mathématiques de l'IHÉS

, Volume 130, Issue 1, pp 1–61 | Cite as

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

  • Søren Galatius
  • Alexander KupersEmail author
  • Oscar Randal-Williams


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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Copyright information

© IHES and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Søren Galatius
    • 1
  • Alexander Kupers
    • 2
    Email author
  • Oscar Randal-Williams
    • 3
  1. 1.Department of MathematicsUniversity of CopenhagenCopenhagen OEDenmark
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK

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