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Spectral algebra models of unstable v_n-periodic homotopy theory

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arxiv 1703.02186 v3 pith:UNM4CHH5 submitted 2017-03-07 math.AT

Mark Behrens , Charles Rezk This is my paper · ORCID
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keywords algebrahomotopyspectralmodelsn-periodicsurveytheoryunstable
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We give a survey of a generalization of Quillen-Sullivan rational homotopy theory which gives spectral algebra models of unstable v_n-periodic homotopy types. In addition to describing and contextualizing our original approach, we sketch two other recent approaches which are of a more conceptual nature, due to Arone-Ching and Heuts. In the process, we also survey many relevant concepts which arise in the study of spectral algebra over operads, including topological Andr\'e-Quillen cohomology, Koszul duality, and Goodwillie calculus.

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  1. The Lubin-Tate Theory of Configuration Spaces: I

    math.AT 2019-08 accept novelty 8.0 of 10

    A new Hecke spectral sequence computes the Morava E-theory of unordered configuration spaces, yielding explicit E-theory and F_p-homology results for p-point configurations.

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