A propos de conjectures de Serre et Sullivan.
An algebraic model for homotopy fibers.
«Autopsie d'un meurtre» dans l'homologie d'une algèbre de chaînes
Dualité d'Eckmann-Hilton à travers les modèles de Chen-Quillen-Sullivan
Formes différentielles et suites spectrales
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.
Homology exponents for -spaces.
Homology Operations in the Eilenberg-Moore Spectral Sequence.
Lusternik-Schnirelmann Category and the Moore Spectral Sequence.
Module derivations and cohomological splitting of adjoint bundles
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 cohomology ring of the free loop space of a wedge of spheres.
On the homology of mapping spaces
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.
Parallelizability of Homogeneous Spaces, II.
Parallelizability of Homogeneous Spaces, II (Erratum).
Profinite spaces and problems of realizability. (Espaces profinis et problèmes de réalisabilité.)
Pro-isomorphisms of homology towers.
Steenrod Operations in the Eilenberg-Moore Spectral Sequence.
The cohomology algebra of certain free loop spaces
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
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....
The Krull filtration on the category and cohomology of spaces. (La filtration de Krull de la categorie et la cohomologie des espaces.)
The Morava -Theory Eilenberg-Moore spectral sequence.