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Calcul Jacobien

Bernard Morin (1975)

Annales scientifiques de l'École Normale Supérieure

Calculation of the avoiding ideal for Σ 1 , 1

Tamás Terpai (2009)

Banach Center Publications

We calculate the mapping H * ( B O ; ) H * ( K 1 , 0 ; ) and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.

Caustics and wave front propagations: applications to differential geometry

Shyuichi Izumiya, Masatomo Takahashi (2008)

Banach Center Publications

This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.

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.

Compositions of equi-dimensional fold maps

Yoshihiro Hirato, Masamichi Takase (2012)

Fundamenta Mathematicae

According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem.

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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