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Displaying similar documents to “Rational fibrations in differential homological algebra.”

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.

A proof of the Baues-Lemaire conjecture in rational homotopy theory

Majewski, Martin

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This paper contains an announcement of a result, which settles the connection between various algebraic models for rational homotopy theory: the models of Quillen, Sullivan and Adams-Hilton-Anick. It is shown how this result, combined with a recent result of Anick, implies a conjecture of and [Math. Ann. 225, 219-245 (1977; Zbl 0322.55019)].We describe in some detail the construction of these models (Section 1). We present a variant of the Adams-Hilton model, which is defined in a...

The rational homotopy of Thom spaces and the smoothing of isolated singularities

Stefan Papadima (1985)

Annales de l'institut Fourier

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Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and...