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Algebraic models for 1-dimensional categories of rational G-spectra

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arxiv 2501.11200 v1 pith:MVU7SF7I submitted 2025-01-20 math.AT

J.P.C.Greenlees This is my paper · ORCID
classification math.AT
keywords dimensionalalgebraicblocksg-spectragroupsmodelsrationalauthor
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In this paper we give algebraic models for rational G-spectra for a compact Lie group G when the geometric isotropy is restricted to lie in a 1-dimensional block of conjugacy classes. This includes all blocks of all groups of dimension 1, semifree spectra, and 1-dimensional blocks for many other groups G. The results were known previously for G=SO(2) or O(2) due to work of Barnes, Shipley and the author.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rational SU(3)-equivariant cohomology theories

    math.AT 2025-02 conditional novelty 6.0 of 10

    Rational SU(3)-equivariant spectra are Quillen equivalent to differential graded objects of an explicitly constructed abelian category A(SU(3)).

  2. An algebraic model for rational U(2)-spectra

    math.AT 2025-02 conditional novelty 6.0 of 10

    The category of rational U(2)-spectra is shown to decompose into seven blocks, each with an explicit algebraic model, yielding a calculable algebraic model for the whole category.

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