Displaying similar documents to “Formality of the function space of free maps into an elliptic space”

Rational homotopy of Serre fibrations

Jean-Claude Thomas (1981)

Annales de l'institut Fourier

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In rational homotopy theory, we show how the homotopy notion of pure fibration arises in a natural way. It can be proved that some fibrations, with homogeneous spaces as fibre are pure fibrations. Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration.

The rational homotopy type of configuration spaces of two points

Pascal Lambrechts, Don Stanley (2004)

Annales de l’institut Fourier

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We prove that the rational homotopy type of the configuration space of two points in a 2 -connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.

Variations on a conjecture of Halperin

Gregory Lupton (1998)

Banach Center Publications

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Halperin has conjectured that the Serre spectral sequence of any fibration that has fibre space a certain kind of elliptic space should collapse at the E 2 -term. In this paper we obtain an equivalent phrasing of this conjecture, in terms of formality relations between base and total spaces in such a fibration (Theorem 3.4). Also, we obtain results on relations between various numerical invariants of the base, total and fibre spaces in these fibrations. Some of our results give weak versions...