A model category structure for equivariant algebraic models
Author:
Laura Scull
Journal:
Trans. Amer. Math. Soc. 360 (2008), 25052525
MSC (2000):
Primary 55P91; Secondary 18G55, 55P62
Published electronically:
November 28, 2007
MathSciNet review:
2373323
Fulltext PDF Free Access
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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 1connected 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:
http://dx.doi.org/10.1090/S0002994707044212
PII:
S 00029947(07)044212
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.
