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Rational $S^1$-equivariant homotopy theory

Author(s): Laura Scull
Journal: Trans. Amer. Math. Soc. 354 (2002), 1-45.
MSC (2000): Primary 55P91, 55P62; Secondary 55R35, 55S45
Posted: May 17, 2001
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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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Additional Information:

Laura Scull
Affiliation: Department of Mathematics, The University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, Michigan 48109-1109
Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Rd., Vancouver, BC V6T 1Z2, Canada
Email: laurass@math.lsa.umich.edu

DOI: 10.1090/S0002-9947-01-02790-8
PII: S 0002-9947(01)02790-8
Keywords: Equivariant homotopy, minimal model, rationalization
Received by editor(s): April 26, 2000
Received by editor(s) in revised form: September 27, 2000
Posted: May 17, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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