We explore the relationship between (non-planar) rooted trees and free trees, i.e. without root. We give in particular, for non-rooted trees, a substitute for the Lie bracket given by the antisymmetrization of the pre-Lie product.

Geir Bogfjellmo Charles H. Curry Dominique Manchon

We exhibit an internal coproduct on the Hopf algebra of finite topologies recently defined by the second author, C. Malvenuto and F. Patras, dual to the composition of "quasi-ormoulds", which are the natural version of J. Ecalle's moulds in this setting. All these results are displayed in the linear species formalism.

Frédéric Fauvet Loïc Foissy Dominique Manchon

We describe four natural operad structures on the vector space generated by isomorphism classes of finite posets. The three last ones are set-theoretical and can be seen as a simplified version of the first, the same way the NAP operad behaves with respect to the pre-Lie operad. Moreover the two first ones are isomorphic.

Frédéric Fauvet Loïc Foissy Dominique Manchon

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure to match the double twisted bialgebra axioms is explicitly described.

Mohamed Ayadi Dominique Manchon

We prove that certain specific sum of enhanced states produce torsion of order two in the Khovanov homology.

R. Díaz P. M. G. Manchón

Nous definissons le front d'onde d'un vecteur-distribution pour une representation unitaire d'un groupe de Lie reel $G$ a l'aide du calcul pseudo-differentiel mis au point dans un travail anterieur. Cette notion precise celle de front d'onde d'une representation introduite par R. Howe. En application nous donnons une condition suffisante pour qu'un vecteur-distribution reste un vecteur-distribution pour la restriction de la representation a un sous-groupe ferme $H$, et nous donnons un theoreme de propagation des singularites pour les vecteurs-distribution.

Dominique Manchon

We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated.

Dominique Manchon

On a flat manifold, M. Kontsevich's formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that its derivative at any formal Poisson 2-tensor induces an isomorphism of graded commutative algebras from Poisson cohomology space to Hochschild cohomology space relative to the associated deformed multiplication. We give here a detailed proof of this result, with signs and orientations precised.

Dominique Manchon Charles Torossian

An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes' and Kreimer's work on renormalization in the context of general connected Hopf algebras, in particular Birkhoff decomposition and, in the graded case, the scattering-type formula.

Dominique Manchon

Nous construisons pour tout corps k de caracteristique zero un foncteur de la categorie des k-espaces vectoriels dans la categorie des k-algebres de Hopf pointees, qui a tout espace vectoriel V associe son algebre de Hopf bitensorielle pointee A(V). Cette algebre de Hopf est graduee, verifie une propriete universelle, et contient une famille remarquable d'elements primitifs P. Nous conjecturons que P engendre l'algebre de Lie des elements primitifs de A(V). Enfin lorsque V est de dimension finie nous mettons en evidence un couplage de Hopf entre A(V) et A(V*) dont le noyau contient l'ideal (de Hopf) engendre par les elements de P de degre au moins egal a 2.

Dominique Manchon