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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A model category structure for equivariant algebraic models
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by Laura Scull PDF
Trans. Amer. Math. Soc. 360 (2008), 2505-2525 Request permission

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
  • 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