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Global homotopy theory via spectral Mackey functors

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arxiv 2202.07272 v2 pith:CVN42F57 submitted 2022-02-15 math.AT math.KT

Tobias Lenz This is my paper · ORCID
classification math.ATmath.KT
keywords globalfunctorsmackeycategoryhomotopyspectraltheoryanalogous
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abstract

We show that Hausmann's model of global stable homotopy theory in terms of symmetric spectra is equivalent to the $\infty$-category of spectral Mackey functors in the sense of Barwick on a certain global effective Burnside category. We moreover provide an analogous description of Schwede's ultra-commutative monoids as space-valued global Mackey functors.

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  1. The spectrum of global representations for families of bounded rank and VI-modules

    math.RT 2025-06 conditional novelty 8.0 of 10

    Compact derived VI-modules are classified by their support types, and the Balmer spectrum for families of bounded-rank abelian p-groups is computed explicitly.

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