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”

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.

On the spectral sequence fo r the $\bar{\partial}$ -cohomology of a holomorpkic bundle with Stein fibres

Guido Lupacciolu (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si esamina la successione spettrale per la $\bar{\partial}$ -coomologia dello spazio totale di un fibrato olomorfo nel caso in cui le fibre siano varietà di Stein.

Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

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The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p > 0$ , an overconvergent de Rham-Witt complex $W^{†} Ω_{X / k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$ , is a complex of étale sheaves and a differential graded algebra over the ring $W^{†} (𝒪_{X})$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

Unstable homotopy invariance for finite fields

Kevin P. Knudson (2002)

Fundamenta Mathematicae

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We prove that if k is a finite field with $p^{d}$ elements, then the natural map $H_{i} (G L ₙ (k), ℤ) \to H_{i} (G L ₙ (k [t]), ℤ)$ is an isomorphism for 0 ≤ i < d(p-1) and for all n.

Suite spectrale du coniveau et $t$ -structure homotopique

Frédéric Déglise (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Dans cette note, nous montrons que la suite spectrale du coniveau associée à un spectre motivique sur un corps parfait coïncide avec sa suite spectrale d’hypercohomologie pour la t-structure homotopique.