On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei

Displaying similar documents to “On some rational fibrations with nonvanishing Massey products over homogeneous spaces”

On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy

Martin Markl (1989)

Annales de l'institut Fourier

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The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type $F$ is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.

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.

Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga, M. Tezuka (1987)

Annales de l'institut Fourier

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We show that an orientable fibration whose fiber has a homotopy type of homogeneous space $G / U$ with rank $G = rang U$ is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of $G$ plays a key role in the proof. We also show that it is valid for mod. $p$ coefficients if $p$ does not divide the order of the Weyl group of $G$ .

Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin

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[For the entire collection see Zbl 0699.00032.] A fibration $F \to E \to B$ is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if $H^{*} (E; k) \to H^{*} (F; k)$ is surjective. This is equivalent to saying that $π_{1} (B)$ acts trivially on $H^{*} (F; k)$ and the Serre spectral sequence collapses at $E^{2}$ . S. Halperin conjectured that for $c h a r (k) = 0$ and F a 1-connected rationally elliptic space (i.e., both $H^{*} (F; 𝒬)$ and $π_{*} (F) \otimes 𝒬$ are finite dimensional) such that $H^{*} (F; k)$ vanishes in odd degrees, every fibration $F \to E \to B$ is TNCZ. The author proves this...

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.

The Hochschild cohomology of a closed manifold

Yves Felix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2004)

Publications Mathématiques de l'IHÉS

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Let M be a closed orientable manifold of dimension and $𝒞^{*} (M)$ be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is a graded commutative and associative algebra. The augmentation map $ε : 𝒞^{*} (M) \to 𝑘$ induces a morphism of algebras $I : H H^{*} (𝒞^{*} (M); 𝒞^{*} (M)) \to H H^{*} (𝒞^{*} (M); 𝑘)$ . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of $H H^{*} (𝒞^{*} (M); 𝑘)$ , which is in general quite small. The algebra $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is expected to...