Rational $S^1$-equivariant homotopy theory
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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.References
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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
- Received by editor(s): April 26, 2000
- Received by editor(s) in revised form: September 27, 2000
- Published electronically: May 17, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1-45
- MSC (2000): Primary 55P91, 55P62; Secondary 55R35, 55S45
- DOI: https://doi.org/10.1090/S0002-9947-01-02790-8
- MathSciNet review: 1859023