Geodesic
An algebraic model for rational toral G–spectra
Barnes, David1 ; Greenlees, John2 ; Kędziorek, Magdalena3
1 Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast, United Kingdom
2 Mathematics Institute, University of Warwick, Coventry, United Kingdom
3 Max Planck Institute for Mathematics, Bonn, Germany, Mathematical Institute, Utrecht University, Utrecht, Netherlands
Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3541-3599

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.3541
Classification : 55N91, 55P42, 55P60
Keywords: equivariant cohomology, rational equivariant spectra, algebraic models, model category

Barnes, David 1 ; Greenlees, John 2 ; Kędziorek, Magdalena 3

1 Mathematical Sciences Research Centre, Queen’s University Belfast, Belfast, United Kingdom
2 Mathematics Institute, University of Warwick, Coventry, United Kingdom
3 Max Planck Institute for Mathematics, Bonn, Germany, Mathematical Institute, Utrecht University, Utrecht, Netherlands 
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Barnes, David; Greenlees, John; Kędziorek, Magdalena. An algebraic model for rational toral G–spectra. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3541-3599. doi: 10.2140/agt.2019.19.3541

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