Le localisateur fondamental minimal
Minimal resolutions and other minimal models.
In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes....
Motivic cell structures.
Motivic symmetric spectra.
Multiplicative maps from Hℤ to a ring spectrum R-a naive version
The paper is devoted to the study of the space of multiplicative maps from the Eilenberg-MacLane spectrum Hℤ to an arbitrary ring spectrum R. We try to generalize the approach of Schwede [Geom. Topol. 8 (2004)], where the case of a very special R was studied. In particular we propose a definition of a formal group law in any ring spectrum, which might be of independent interest.
Non functorial cylinders in a model category
Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids.
Normalizing the cyclic modules of Connes.
Note on homotopy pullbacks in abelian categories
Oka manifolds: From Oka to Stein and back
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...
On a conjecture by J. H. Smith.
On a theory of braided cochains in algebraic topology (Preliminary version). (Sur une théorie des cochaines tresses en topologie algébrique (Version préliminaire ).)
On modified Reedy and modified projective model structures.
On Neeman's well generated triangulated categories.
On the classification of Moore algebras and their deformations.
On the derived category of sheaves on a manifold.
On the homology of small categories and asynchronous transition systems.
On the preservation of homotopy invariance by Kan extensions
On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.
On weak -homotopy equivalences of modules
Si definisce il gruppo di —omotopia di un singolo modulo e si introduce la nozione di equivalenza -omotopica debole. Sotto determinate condizioni per l'anello di base oppure per i moduli considerati, le equivalenze -omotopiche deboli coincidono con le equivalenze -omotopiche (forti).
Quillen's theory for algebraic models of n-types.