Volume 16, issue 4 (2016)

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Rational equivariant cohomology theories with toral support

J P C Greenlees

Algebraic & Geometric Topology 16 (2016) 1953–2019
Abstract

For an arbitrary compact Lie group $G$, we describe a model for rational $G$–spectra with toral geometric isotropy and show that there is a convergent Adams spectral sequence based on it. The contribution from geometric isotropy at a subgroup $K$ of the maximal torus of $G$ is captured by a module over ${H}^{\ast }\left(B{W}_{G}^{e}\left(K\right)\right)$ with an action of ${\pi }_{0}\left({W}_{G}\left(K\right)\right)$, where ${W}_{G}^{e}\left(K\right)$ is the identity component of ${W}_{G}\left(K\right)={N}_{G}\left(K\right)∕K$.

Keywords
rational equivariant spectra, algebraic models, Adams spectral sequence, reduction to torus normalizer
Mathematical Subject Classification 2010
Primary: 55N91, 55P42, 55P91
Secondary: 55P92, 55T15