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Connections of higher order and product preserving functors

Jacek Gancarzewicz, Noureddine Rahmani, Modesto R. Salgado (2002)

Czechoslovak Mathematical Journal

In this paper we consider a product preserving functor of order r and a connection Γ of order r on a manifold M . We introduce horizontal lifts of tensor fields and linear connections from M to ( M ) with respect to Γ . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

Constantes de Sobolev des arbres

Marc Bourdon (2007)

Bulletin de la Société Mathématique de France

Étant donnés p [ 1 , + [ et un arbre T dont chaque sommet est de valence au moins  3 , on étudie la constante de Sobolev d’exposant p de T , c’est-à-dire la plus petite constante σ p telle que pour tout u p ( T 0 ) on ait u p p σ p d u p p . Notre motivation vient de la recherche de graphes finis avec des petites constantes de Poincaré d’exposant  p , en vue d’obtenir des exemples de groupes qui ont la propriété de point fixe sur les espaces L p .

Constructing generic smooth maps of a manifold into a surface with prescribed singular loci

Osamu Saeki (1995)

Annales de l'institut Fourier

It is known that the singular set S ( f ) of a generic smooth map f : M N of an n -dimensional manifold into a surface is a closed 1-dimensional submanifold of M and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.

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