Displaying similar documents to “A rational splitting of a based mapping 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.

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...

Homotopy Lie algebras and fundamental groups via deformation theory

Martin Markl, Stefan Papadima (1992)

Annales de l'institut Fourier

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We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as π * Ω S (the homotopy Lie algebra) or gr * π 1 S (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.