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Cellular $E_k$-algebras

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arxiv 1805.07184 v4 pith:WXVUUBM2 submitted 2018-05-18 math.AT

Soren Galatius , Alexander Kupers , Oscar Randal-Williams This is my paper · ORCID
classification math.AT
keywords algebrasapplicationscellularapproximationscomputationalconceptualconvenientespecially
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abstract

We give a set of foundations for cellular $E_k$-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such as filtrations, a homology theory for $E_k$-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers.

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  1. Representation stability for ordered Hurwitz spaces

    math.AT 2025-09 conditional novelty 7.0 of 10

    The homology groups of ordered Hurwitz spaces, seen as representations of symmetric groups, have stable multiplicities in a range that grows linearly with homological degree.

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