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Cobordisme fibré et approximation d’une sous-variété singulière par des sous-variétés C

André Didierjean (1983)

Annales de l'institut Fourier

Dans cet article, on montre comment le cobordisme d’applications et le cobordisme fibré fournissent les obstructions à des problèmes de lissage topologique de singularités avec un lieu singulier compact. On calcule dans le cas des petites dimensions les groupes de cobordisme fibré. Les résultats connus sur le cobordisme fibré ou sur son image dans le cobordisme d’application permettent le calcul d’un certain nombre de ces obstructions.

Cobordisms of fold maps of 2k+2-manifolds into 3 k + 2

Tamás Terpai (2008)

Banach Center Publications

We calculate the group of cobordisms of k-codimensional maps into Euclidean space with no singularities more complicated than fold for a 2k+2-dimensional source manifold in both oriented and unoriented cases.

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of is isomorphic to Z , then is without holonomy. We also show that if π 2 ( M ) 0 and the fundamental group of each leaf of is isomorphic to Z k ( k Z 0 ), then is without holonomy.

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

We provide a simple characterization of codimension two submanifolds of n ( ) that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when n 6 . If the codimension two submanifold is a nonsingular algebraic subset of n ( ) whose Zariski closure in n ( ) is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in n ( ) .

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