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

Martin Markl

Displaying similar documents to “On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy”

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.

The homotopy Lie algebra for finite complexes

Yves Félix, Stephen Halperin, Jean-Claude Thomas (1982)

Publications Mathématiques de l'IHÉS

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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 $S^{2} \to E \to ℂ P^{3}$ 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: $a b \neq D (x^{2} y))$ . In fact, for any rational fibration $S^{2} \to E \to ℂ P^{3}$ the...

Homotopy Lie algebras and Poincaré series of algebras with monomial relations.

Avramov, Luchezar L. (2002)

Homology, Homotopy and Applications

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Graded Lie algebras with finite polydepth

Yves Felix, Stephen Halperin, Jean-Claude Thomas (2003)

Annales scientifiques de l'École Normale Supérieure

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Homotopy Lie algebras; lower central series and the Koszul property.

Papadima, Stefan, Suciu, Alexander I. (2004)

Geometry & Topology

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The center of a graded connected Lie algebra is a nice ideal

Yves Félix (1996)

Annales de l'institut Fourier

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Let $(𝕃 (V), d)$ be a free graded connected differential Lie algebra over the field $ℚ$ of rational numbers. An ideal $I$ in the Lie algebra $H (𝕃 (V), d)$ is called if, for every cycle $α \in 𝕃 (V)$ such that $[α]$ belongs to $I$ , the kernel of the map $H (𝕃 (V), d) \to H (𝕃 (V \oplus ℚ x), d)$ , $d (x) = α$ , is contained in $I$ . We show that the center of $H (𝕃 (V), d)$ is a nice ideal and we give in that case some informations on the structure of the Lie algebra $H (𝕃 (V \oplus ℚ x), d)$ . We apply this computation for the determination of the rational homotopy Lie algebra $L_{X} = π_{*} (Ω X) \otimes ℚ$ of a simply connected space $X$ . We deduce...