-space structure on pointed mapping spaces.
On spaces of the same strong -type.
The center of a graded connected Lie algebra is a nice ideal
Let be a free graded connected differential Lie algebra over the field of rational numbers. An ideal in the Lie algebra is called if, for every cycle such that belongs to , the kernel of the map , , is contained in . We show that the center of is a nice ideal and we give in that case some informations on the structure of the Lie algebra . We apply this computation for the determination of the rational homotopy Lie algebra of a simply connected space . We deduce that the kernel...
Growth and Lie brackets in the homotopy Lie algebra.
Loop space homology of spaces of LS category one and two.
Sur l'homologie de l'espace des lacets d'une variété compacte
The Formal Dimension of a Toplogical Space.
Module d'holonomie d'une fibration
Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets
Un des problèmes historiques de la théorie homotopique des espaces est de mesurer l’effet de l’attachement d’une cellule au niveau des groupes d’homotopie. Le problème de l’attachement inerte reste en particulier un problème ouvert. Nous donnons ici une réponse partielle à ce problème.
Homologie des espaces de lacets des espaces de configuration
Nous calculons dans ce texte l’homologie de l’espace des lacets de l’espace des configurations ordonnées de points dans une variété compacte simplement connexe .
Rational BV-algebra in string topology
Let be a 1-connected closed manifold of dimension and be the space of free loops on . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of , . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between and the shifted homology . We also prove that the...
Nilpotent subgroups of the group of fibre homotopy equivalences.
Let ξ = (E, p, B, F) be a Hurewicz fibration. In this paper we study the space L(ξ) consisting of fibre homotopy self equivalences of ξ inducing by restriction to the fibre a self homotopy equivalence of F belonging to the group G. We give in particular conditions implying that π(L(ξ)) is finitely generated or that L(ξ) has the same rational homotopy type as aut(F).
Lefschetz number and degree of a self-map
The Hochschild cohomology of a closed manifold
Let M be a closed orientable manifold of dimension and be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic...
The homotopy Lie algebra for finite complexes
L. S. catégorie et suite spectrale de Milnor-Moore. (Une nuit dans le train)
Sur certaines algèbres de Lie de dérivations
Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.
Graded Lie algebras with finite polydepth
Rational string topology
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in . Some explicit computations of the loop product and the string bracket are given.
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