Lectures on minimal models
Localization of nilpotent fibre maps.
LS category of classifying spaces and 2-cones.
LS-catégorie de CW-complexes à 3 cellules en théorie homototique R-locale.
We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S2n Uk[i2n,i2n] e4n. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.
LS-category of classifying spaces.
LS-category of classifying spaces. II.
Minimal models for non-nilpotent spaces.
Minimal Models of Loop spaces and suspensions.
Minimal models of oriented Grassmannians and applications
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....
Mixed Hodge Structures on the Homotopy of Links.
Mod p loop space homology.
Moduli spaces for fundamental groups and Link invariants derived from the lower central series.
Nilpotent completions and Lie rings associated to link groups.
Nilpotent complex structures.
Este artículo presenta un panorama de algunos resultados recientes sobre estructuras complejas nilpotentes J definidas sobre nilvariedades compactas. Tratamos el problema de clasificación de nilvariedades compactas que admiten una tal J, el estudio de un modelo minimal de Dolbeault y su formalidad, y la construcción de estructuras complejas nilpotentes para las cuales la sucesión espectral de Frölicher no colapsa en el segundo término.
Note on the rational cohomology of the function space of based maps.
On compact symplectic and Kählerian solvmanifolds which are not completely solvable
We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.
On Davis-Januszkiewicz homotopy types I: formality and rationalisation.
On -disconnected injective models
Let be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the -connected case is incorrect because of an error concerning algebraic properties. In the -disconnected case the orbit category was originally replaced by the category with one object for each component of each fixed point simplicial subsets of a -simplicial set , for all subgroups . We redefine the equivariant minimality and redevelop some results on the rational homotopy...
On Hochschild and cyclic homology of certain homogeneous spaces