Algebraic & Geometric Topology

Rational equivariant cohomology theories with toral support

J P C Greenlees

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

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 4 (2016), 1953-2019.

Dates
Received: 15 January 2015
Revised: 29 October 2015
Accepted: 6 November 2015
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895905

Digital Object Identifier
doi:10.2140/agt.2016.16.1953

Mathematical Reviews number (MathSciNet)
MR3546456

Zentralblatt MATH identifier
1358.55004

Subjects
Primary: 55N91: Equivariant homology and cohomology [See also 19L47] 55P42: Stable homotopy theory, spectra 55P91: Equivariant homotopy theory [See also 19L47]
Secondary: 55P92: Relations between equivariant and nonequivariant homotopy theory 55T15: Adams spectral sequences

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

Citation

Greenlees, J P C. Rational equivariant cohomology theories with toral support. Algebr. Geom. Topol. 16 (2016), no. 4, 1953--2019. doi:10.2140/agt.2016.16.1953. https://projecteuclid.org/euclid.agt/1511895905


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