2001
DOI: 10.1090/s0002-9947-01-02790-8
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Rational 𝑆¹-equivariant homotopy theory

Abstract: Abstract. We give an algebraicization of rational S 1 -equivariant homotopy theory. There is an algebraic category of "T-systems" which is equivalent to the homotopy category of rational S 1 -simply connected S 1 -spaces. There is also a theory of "minimal models" for T-systems, analogous to Sullivan's minimal algebras. Each S 1 -space has an associated minimal T-system which encodes all of its rational homotopy information, including its rational equivariant cohomology and Postnikov decomposition.

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Cited by 12 publications
(17 citation statements)
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“…This section contains a brief summary of the major results of the author [11] on T 1 -minimal models, and the results of Mandell and the author in extending these to Abelian compact Lie groups. These models are used directly in one of the definitions of T-equivariant formality.…”
Section: Equivariant Algebraic Modelsmentioning
confidence: 99%
See 4 more Smart Citations
“…This section contains a brief summary of the major results of the author [11] on T 1 -minimal models, and the results of Mandell and the author in extending these to Abelian compact Lie groups. These models are used directly in one of the definitions of T-equivariant formality.…”
Section: Equivariant Algebraic Modelsmentioning
confidence: 99%
“…The restriction to the injective objects of the category makes sense geometrically, and it is needed for the existence of minimal models. To establish the equivariant analogue of minimality, we use the idea of an "elementary extension" (defined in [11], Section 11), which builds systems of CDGAs out of diagrams of vector spaces. If M and M ′ are two minimal T-systems and ρ : M → A and ρ ′ : M ′ → A are quasi-isomorphisms, then there is an isomorphism f :…”
Section: Equivariant Algebraic Modelsmentioning
confidence: 99%
See 3 more Smart Citations