Calcul Jacobien
Calculation of the avoiding ideal for
We calculate the mapping 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
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.
Classification des germes à point critique isolé et à nombres de modules 0 ou 1
Classification of singularities with compact abelian symmetry
Cobordism of immersions and singular maps, loop spaces and multiple points
Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs.
Cobordisms of fold maps of 2k+2-manifolds into
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
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
It is known that the singular set of a generic smooth map of an -dimensional manifold into a surface is a closed 1-dimensional submanifold of 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.
Contribution à une théorie de Smale à un paramètre dans le cas non simplement connexe
Critical sets of 2-dimensional compact manifolds.
Curves and surfaces in real projective spaces: an approach to generic projections