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Transactions of the American Mathematical Society

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A model category structure for equivariant algebraic models

Author: Laura Scull
Journal: Trans. Amer. Math. Soc. 360 (2008), 2505-2525
MSC (2000): Primary 55P91; Secondary 18G55, 55P62
Published electronically: November 28, 2007
MathSciNet review: 2373323
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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.

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Additional Information

Laura Scull
Affiliation: Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada

Keywords: Equivariant homotopy, minimal model, rational homotopy theory, model category
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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