On the rational homotopy type of function spaces. (English) Zbl 0927.55012

The main result of this paper is the construction of a minimal model for the function space \({\mathcal F}(X,Y)\) of continuous functions from a finite type, finite dimensional space \(X\) to a finite type, nilpotent space \(Y\) in terms of Sullivan’s minimal models for \(X\) and \(Y\). Such constructions appeared in papers of A. Haefliger (1982), M. Vigué-Poirrier (1986), A. Bousfield, C. Peterson and L. Smith (1989), all of them in the bibliography. A version mixing coalgebras and Lie algebras is also performed in [H. Scheerer and D. Tanré, Arch. Math. 59, No. 2, 130-145 (1992; Zbl 0729.55008].


55P15 Classification of homotopy type
55P62 Rational homotopy theory
Full Text: DOI


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[8] Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269 – 331 (1978). · Zbl 0374.57002
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[10] Micheline Vigué-Poirrier, Cohomologie de l’espace des sections d’un fibré et cohomologie de Gelfand-Fuchs d’une variété, Algebra, algebraic topology and their interactions (Stockholm, 1983) Lecture Notes in Math., vol. 1183, Springer, Berlin, 1986, pp. 371 – 396 (French). · Zbl 0591.55004 · doi:10.1007/BFb0075471
[11] Micheline Vigué-Poirrier, Sur l’homotopie rationnelle des espaces fonctionnels, Manuscripta Math. 56 (1986), no. 2, 177 – 191 (French, with English summary). · Zbl 0597.55008 · doi:10.1007/BF01172155
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