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

DOI:
https://doi.org/10.1090/S0002-9947-07-04421-2

Published electronically:
November 28, 2007

MathSciNet review:
2373323

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Abstract | References | Similar Articles | Additional Information

Abstract: In the equivariant category of spaces with an action of a finite group, algebraic `minimal models' exist which describe the rational homotopy for -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 -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

Email:
scull@math.ubc.ca

DOI:
https://doi.org/10.1090/S0002-9947-07-04421-2

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.