Spectral sequences for commutative Lie algebras

Friedrich Wagemann

Displaying similar documents to “Spectral sequences for commutative Lie algebras”

André-Quillen cohomology for commutative coalgebras

Jolanta Słomińska (1975)

Colloquium Mathematicae

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The complex oriented cohomology of extended powers

John Robert Hunton (1998)

Annales de l'institut Fourier

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We examine the behaviour of a complex oriented cohomology theory $G^{*} (-)$ on $D_{p} (X)$ , the $C_{p}$ -extended power of a space $X$ , seeking a description of $G^{*} (D_{p} (X))$ in terms of the cohomology $G^{*} (X)$ . We give descriptions for the particular cases of Morava $K$ -theory $K (n)$ for any space $X$ and for complex cobordism $M U$ , the Brown-Peterson theories BP and any Landweber exact theory for a wide class of spaces.

A review of Lie superalgebra cohomology for pseudoforms

Carlo Alberto Cremonini (2022)

Archivum Mathematicum

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This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational...

Leibniz cohomology for differentiable manifolds

Jerry M. Lodder (1998)

Annales de l'institut Fourier

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We propose a definition of Leibniz cohomology, $H L^{*}$ , for differentiable manifolds. Then $H L^{*}$ becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of $H L^{*} (R^{n}; R)$ reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

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...

A spectral sequence for de Rham cohomology

Bingyong Xie (2011)

Acta Arithmetica

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Algebras of the cohomology operations in some cohomology theories

A. Jankowski

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Contents0. Introduction............................................................................................................................................. 51. Preliminaries.......................................................................................................................................... 62. Generalized cohomology theories with a coefficient group $Z_{p}$ .............................................. 83. Cohomology theory BP* ( , $Z_{p}$ )........................................................................................................

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

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This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension $\leq 4$ and $\geq 11$ . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real...

Salvetti complex, spectral sequences and cohomology of Artin groups

Filippo Callegaro (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.

Applications of weight-two motivic cohomology.

Kahn, Bruno (1996)

Documenta Mathematica

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