Cohomology of $BO(n_1)\times \dots \times BO(n_m)$ with local integer coefficients

Richard Lastovecki

Displaying similar documents to “Cohomology of $B O (n_{1}) \times \dots \times B O (n_{m})$ with local integer coefficients”

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...

A geometric description of differential cohomology

Ulrich Bunke, Matthias Kreck, Thomas Schick (2010)

Annales mathématiques Blaise Pascal

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In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [, , , ]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in []. There the starting point was Quillen’s cobordism description of singular...

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

Bundles, cohomology and truncated symmetric polynomials.

Adem, Alejandro, Reichstein, Zinovy (2010)

Documenta Mathematica

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$Z_{p}$ -cohomology manifold with no $Z_{p}$ -resolution

W. Jakobsche (1991)

Fundamenta Mathematicae

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Unramified cohomology of alternating groups

Fedor Bogomolov, Tihomir Petrov (2011)

Open Mathematics

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We prove vanishing results for the unramified stable cohomology of alternating groups.

On the cohomology of the classifying space of the gauge group over some 4-complexes

Gregor Masbaum (1991)

Bulletin de la Société Mathématique de France

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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...

Displaying similar documents to “Cohomology of B O ( n 1 ) × ⋯ × B O ( n m ) with local integer coefficients”

Displaying similar documents to “Cohomology of $B O (n_{1}) \times \dots \times B O (n_{m})$ with local integer coefficients”