Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin

Displaying similar documents to “Towards one conjecture on collapsing of the Serre spectral sequence”

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...

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.

An example of a fiber in fibrations whose Serre spectral sequences collapse

Toshihiro Yamaguchi (2005)

Czechoslovak Mathematical Journal

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We give an example of a space $X$ with the property that every orientable fibration with the fiber $X$ is rationally totally non-cohomologous to zero, while there exists a nontrivial derivation of the rational cohomology of $X$ of negative degree.

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* ( , $Z_{p}$ )........................................................................................................

A $G$ -minimal model for principal $G$ -bundles

Shrawan Kumar (1982)

Annales de l'institut Fourier

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Sullivan associated a uniquely determined $D G A |_{Q}$ to any simply connected simplicial complex $E$ . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space $E$ . In case $E$ is the total space of a principal $G$ -bundle, ( $G$ is a compact connected Lie-group) we associate a $G$ -equivariant model $U_{G} [E]$ , which is a collection of “ $G$ -homotopic” $D G A$ ’s $|_{R}$ with $G$ -action. $U_{G} [E]$ will, in general, be different from the Sullivan’s minimal model of the space $E$ . $U_{G} [E]$ contains the...

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...

Cohomology $C_{\infty}$ -algebra and rational homotopy type

Tornike Kadeishvili (2009)

Banach Center Publications

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In the rational cohomology of a 1-connected space a structure of $C_{\infty}$ -algebra is constructed and it is shown that this object determines the rational homotopy type.

Spectral sequences for commutative Lie algebras

Friedrich Wagemann (2020)

Communications in Mathematics

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We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic $2$ . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.