An algebraic model for rational toral G-spectra

Barnes, David; Greenlees, J. P. C.; Kędziorek, Magdalena

doi:10.2140/agt.2019.19.3541

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An algebraic model for rational toral G-spectra

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Kędziorek, Magdalena
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Barnes, D., Greenlees, J. P. C., & Kędziorek, M. (2019). An algebraic model for rational toral G-spectra. Algebraic & Geometric Topology, 19(7), 3541-3599. doi:10.2140/agt.2019.19.3541.

Cite as: https://hdl.handle.net/21.11116/0000-0006-3F33-B

Abstract

For G a compact Lie group, toral G–spectra are those rational G–spectra whose
geometric isotropy consists of subgroups of a maximal torus of G. The homotopy
category of rational toral G–spectra is a retract of the category of all rational G–
spectra.
We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016)
1953–2019) gives an algebraic model for the toral part of rational G–spectra. This
is a major step in establishing an algebraic model for all rational G–spectra for any
compact Lie group G.