Formality of the function space of free maps into an elliptic space
Free actions on products of spheres: The rational case.
Ganea fibrations. (Fibrations à la Ganea.)
Generalized symmetric spaces and minimal models
We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.
Genus sets and SNT sets of certain connective covering spaces
We study the genus and SNT sets of connective covering spaces of familiar finite CW-complexes, both of rationally elliptic type (e.g. quaternionic projective spaces) and of rationally hyperbolic type (e.g. one-point union of a pair of spheres). In connection with the latter situation, we are led to an independently interesting question in group theory: if f is a homomorphism from Gl(ν,A) to Gl(n,A), ν < n, A = ℤ, resp. , does the image of f have infinite, resp. uncountably infinite, index in...
Graded Lie Algebras of depth one.
Graded Lie algebras with finite polydepth
Growth and Lie brackets in the homotopy Lie algebra.
-space structure on pointed mapping spaces.
Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces
Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of , and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same -type problems and giving us an information about the rational homotopy...
Homotopie des espaces de concordances
Homotopie rationnelle et croissance du nombre de géodésiques fermées
Homotopy Lie algebra of classifying spaces for hyperbolic coformal 2-cones.
Homotopy Lie algebras; lower central series and the Koszul property.
Hopf algebras up to homotopy and the Bockstein spectral sequence.
Injective models of -disconnected simplicial sets
We generalize the results by G.V. Triantafillou and B. Fine on -disconnected simplicial sets. An existence of an injective minimal model for a complete -algebra is presented, for any -category . We then make use of the -category associated with a -simplicial set to apply these results to the category of -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent -simplicial set by means of its injective minimal model.
Iterated Integrals and Homotopy Periods
Joins of DGA modules and sectional category.
Koszul DG-algebras Arising from Configuration Spaces.
L. S. catégorie et suite spectrale de Milnor-Moore. (Une nuit dans le train)