An algebraic model for rational toral G-spectra

David Barnes; John Greenlees; Magdalena Kedziorek

doi:10.2140/agt.2019.19.3541

An algebraic model for rational toral G-spectra

David Barnes, John Greenlees, Magdalena Kedziorek

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

87 Downloads (Pure)

Abstract

For G a compact Lie group, toral G–spectra are those rational G–spectra whose geometric isotropy consists of subgroups of a maximal torus of G. The homotopy category of rational toral G–spectra is a retract of the category of all rational G–spectra.

We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016) 1953–2019) gives an algebraic model for the toral part of rational G–spectra. This is a major step in establishing an algebraic model for all rational G–spectra for any compact Lie group G.

Original language	English
Pages (from-to)	3541–3599
Journal	Algebraic and Geometric Topology
Volume	19
Issue number	7
Early online date	17 Dec 2019
DOIs	https://doi.org/10.2140/agt.2019.19.3541
Publication status	Published - 17 Dec 2019

Access to Document

10.2140/agt.2019.19.3541Licence: Unspecified

An algebraic model for rational toral G-spectra
Copyright 2019 Mathematical Sciences Publishers. This work is made available online in accordance with the publisher’s policies. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 687 KBLicence: Unspecified

David Barnes
- d.barnesqub.acuk
- School of Mathematics and Physics - Senior Lecturer
- Mathematical Sciences Research Centre
Person: Academic

Cite this

@article{0eb389eadc884452bea8e2c90950b3e0,

title = "An algebraic model for rational toral G-spectra",

abstract = "For G a compact Lie group, toral G–spectra are those rational G–spectra whose geometric isotropy consists of subgroups of a maximal torus of G. The homotopy category of rational toral G–spectra is a retract of the category of all rational G–spectra.We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016) 1953–2019) gives an algebraic model for the toral part of rational G–spectra. This is a major step in establishing an algebraic model for all rational G–spectra for any compact Lie group G.",

author = "David Barnes and John Greenlees and Magdalena Kedziorek",

year = "2019",

month = dec,

day = "17",

doi = "10.2140/agt.2019.19.3541",

language = "English",

volume = "19",

pages = "3541–3599",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Agriculture.gr",

number = "7",

}

TY - JOUR

T1 - An algebraic model for rational toral G-spectra

AU - Barnes, David

AU - Greenlees, John

AU - Kedziorek, Magdalena

PY - 2019/12/17

Y1 - 2019/12/17

N2 - For G a compact Lie group, toral G–spectra are those rational G–spectra whose geometric isotropy consists of subgroups of a maximal torus of G. The homotopy category of rational toral G–spectra is a retract of the category of all rational G–spectra.We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016) 1953–2019) gives an algebraic model for the toral part of rational G–spectra. This is a major step in establishing an algebraic model for all rational G–spectra for any compact Lie group G.

AB - For G a compact Lie group, toral G–spectra are those rational G–spectra whose geometric isotropy consists of subgroups of a maximal torus of G. The homotopy category of rational toral G–spectra is a retract of the category of all rational G–spectra.We show that the abelian category of Greenlees (Algebr. Geom. Topol. 16 (2016) 1953–2019) gives an algebraic model for the toral part of rational G–spectra. This is a major step in establishing an algebraic model for all rational G–spectra for any compact Lie group G.

U2 - 10.2140/agt.2019.19.3541

DO - 10.2140/agt.2019.19.3541

M3 - Article

VL - 19

SP - 3541

EP - 3599

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 7

ER -

An algebraic model for rational toral G-spectra

Abstract

Access to Document

Fingerprint

Profiles

David Barnes

Cite this