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Formes différentielles et suites spectrales

Pierre-Paul Grivel (1979)

Annales de l'institut Fourier

La théorie de Sullivan de l’homotopie rationnelle introduit l’algèbre des formes différentielles sur un ensemble simplicial. On montre dans cet article qu’en filtrant cette algèbre on peut obtenir une suite spectrale analogue à celle de Serre. On applique ce résultat pour étudier le modèle minimal d’un fibré et pour obtenir une nouvelle démonstration de la suite spectrale d’Eilenberg-Moore.

Module derivations and cohomological splitting of adjoint bundles

Akira Kono, Katsuhiko Kuribayashi (2003)

Fundamenta Mathematicae

Let G be a finite loop space such that the mod p cohomology of the classifying space BG is a polynomial algebra. We consider when the adjoint bundle associated with a G-bundle over M splits on mod p cohomology as an algebra. In the case p = 2, an obstruction for the adjoint bundle to admit such a splitting is found in the Hochschild homology concerning the mod 2 cohomologies of BG and M via a module derivation. Moreover the derivation tells us that the splitting is not compatible with the Steenrod...

On the homology of mapping spaces

Semën Podkorytov (2011)

Open Mathematics

Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.

The cohomology algebra of certain free loop spaces

Toshihiro Yamaguchi, Katsuhiko Kuribayashi (1997)

Fundamenta Mathematicae

Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of...

The Hochschild cohomology ring of the singular cochain algebra of a space

Katsuhiko Kuribayashi (2011)

Annales de l’institut Fourier

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra....

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