Rational equivariant cohomology theories with toral support

Abstract

For an arbitrary compact Lie group GG, we describe a model for rational GG–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 KK of the maximal torus of GG is captured by a module over H∗(BWeG(K))H∗(BWGe(K)) with an action of π0(WG(K))π0(WG(K)), where WeG(K)WGe(K) is the identity component of WG(K)=NG(K)∕KWG(K)=NG(K)∕K.

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Item Type:	Article
Authors/Creators:	Greenlees, J. https://orcid.org/0000-0002-9855-3337
Copyright, Publisher and Additional Information:	© 2015 Mathematical Sciences Publishers (MSP). This is an author produced version of a paper subsequently published in Algebraic and Geometric Topology. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	rational equivariant spectra; algebraic models; Adams spectral sequence; reduction to torus normalizer
Dates:	Accepted: 6 November 2015 Published (online): 12 September 2016 Published: 12 September 2016
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Funding Information:	Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/C52084X/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/H040692/1
Depositing User:	Symplectic Sheffield
Date Deposited:	14 Dec 2016 10:28
Last Modified:	24 Mar 2018 15:48
Published Version:	http://dx.doi.org/10.2140/agt.2016.16.1953
Status:	Published
Publisher:	Mathematical Sciences Publishers (MSP)
Refereed:	Yes
Identification Number:	10.2140/agt.2016.16.1953
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:109066

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Rational equivariant cohomology theories with toral support

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