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.

Metadata

Authors/Creators:

Greenlees, J. https://orcid.org/0000-0002-9855-3337

© 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:

https://doi.org/10.2140/agt.2016.16.1953

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Rational equivariant cohomology theories with toral support

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