Basic constructions in rational homotopy theory of function spaces
نویسندگان
چکیده
منابع مشابه
André–Quillen cohomology and rational homotopy of function spaces
We develop a simple theory of André–Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework. © 2004 Elsevier Inc. All rights reserved.
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1 The Sullivan model 1.1 Rational homotopy theory of spaces We will restrict our attention to simply-connected spaces. Much of this goes through with nilpotent spaces, but this will keep things easier and less technical. Definition 1. A 1-connected space X is said to be rational if either of the following equivalent conditions holds: 1. π∗X forms a graded Q-vector space. 2. H̃∗X forms a graded Q...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2006
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2201