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A model category structure for equivariant algebraic models
Author(s):
Laura
Scull
Journal:
Trans. Amer. Math. Soc.
360
(2008),
2505-2525.
MSC (2000):
Primary 55P91;
Secondary 18G55, 55P62
Posted:
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  -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:
10.1090/S0002-9947-07-04421-2
PII:
S 0002-9947(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
Posted:
November 28, 2007
Additional Notes:
The author was supported in part by the NSERC
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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