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Rational equivariant cohomology theories with toral support

J P C Greenlees

Algebraic & Geometric Topology 16 (2016) 1953–2019

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(BWGe(K)) with an action of π0(WG(K)), where WGe(K) is the identity component of WG(K) = NG(K)K.

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rational equivariant spectra, algebraic models, Adams spectral sequence, reduction to torus normalizer
Mathematical Subject Classification 2010
Primary: 55N91, 55P42, 55P91
Secondary: 55P92, 55T15
Received: 15 January 2015
Revised: 29 October 2015
Accepted: 6 November 2015
Published: 12 September 2016
J P C Greenlees
School of Mathematics and Statistics
University of Sheffield
Hicks Building
Sheffield S3 7RH
United Kingdom