Displaying similar documents to “The rational homotopy type of configuration spaces of two points”

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.

On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei

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The main result of this brief note asserts, incorrectly, that there exists a rational fibration S 2 → E → ℂ P 3 whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: a b ≠ D ( x 2 y ) ) . In fact, for any rational fibration S 2 → E → ℂ P 3 the...