A model category structure for equivariant algebraic models
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Abstract:
In the equivariant category of spaces with an action of a finite group, algebraic ‘minimal models’ exist which describe the rational homotopy for $G$-spaces which are 1-connected and of finite type. These models are diagrams of commutative differential graded algebras. In this paper we prove that a model category structure exists on this diagram category in such a way that the equivariant minimal models are cofibrant objects. We show that with this model structure, there is a Quillen equivalence between the equivariant category of rational $G$-spaces satisfying the above conditions and the algebraic category of the models.References
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Additional Information
- Laura Scull
- Affiliation: Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada
- Email: scull@math.ubc.ca
- Received by editor(s): March 19, 2005
- Received by editor(s) in revised form: February 10, 2006
- Published electronically: November 28, 2007
- Additional Notes: The author was supported in part by the NSERC
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 2505-2525
- MSC (2000): Primary 55P91; Secondary 18G55, 55P62
- DOI: https://doi.org/10.1090/S0002-9947-07-04421-2
- MathSciNet review: 2373323