Rational equivariant cohomology theories with toral support

Greenlees, J P C

doi:10.2140/agt.2016.16.1953

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Rational equivariant cohomology theories with toral support

J P C Greenlees

Algebraic & Geometric Topology 16 (2016) 1953–2019

DOI: 10.2140/agt.2016.16.1953

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 $H^{*} (B W_{G}^{e} (K))$ with an action of $π_{0} (W_{G} (K))$ , where $W_{G}^{e} (K)$ is the identity component of $W_{G} (K) = N_{G} (K) ∕ K$ .

Keywords

rational equivariant spectra, algebraic models, Adams spectral sequence, reduction to torus normalizer

Mathematical Subject Classification 2010

Primary: 55N91, 55P42, 55P91

Secondary: 55P92, 55T15

References

Publication

Received: 15 January 2015

Revised: 29 October 2015

Accepted: 6 November 2015

Published: 12 September 2016

Authors

J P C Greenlees
School of Mathematics and Statistics University of Sheffield Hicks Building Sheffield S3 7RH United Kingdom

Volume 16, issue 4 (2016)