Rational 𝑆¹-equivariant homotopy theory

Scull, Laura

doi:10.1090/S0002-9947-01-02790-8

Rational $S^1$-equivariant homotopy theory
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by Laura Scull PDF

Trans. Amer. Math. Soc. 354 (2002), 1-45 Request permission

Abstract:

We give an algebraicization of rational $S^1$-equivariant homotopy theory. There is an algebraic category of “$\mathbb {T}$-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 $\mathbb {T}$-systems, analogous to Sullivan’s minimal algebras. Each $S^1$-space has an associated minimal $\mathbb {T}$-system which encodes all of its rational homotopy information, including its rational equivariant cohomology and Postnikov decomposition.

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