Rational 𝑆¹-equivariant homotopy theory

Abstract

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