Simply-connected algebraic surfaces of positive index.
Singular fibers of stable maps and signatures of 4-manifolds.
Singular foliations with Ehresmann connections and their holonomy groupoids
We introduce topological 𝒬-holonomy groupoids for singular foliations (M,ℱ) with an Ehresmann connection 𝒬 using 𝒬-holonomy groups, which have a global character. We show advantage of our groupoids over known ones.
Singular Lefschetz pencils.
Singular open book structures from real mappings
We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
Singular perturbations in foliations.
Singularité générique des applications différentiables de la 2-sphère dans une 3-variété différentiable
Dans cet article nous étudions les singularités des applications différentiables de la deux sphère dans une trois variété avec les méthodes de transversalité et nous utilisons les résultats obtenus pour reprendre dans le cas différentiable, les démonstrations de Papakyriakopoulos et de Whitehead du théorème de la sphère.
Singularities and duality in the flat geometry of submanifolds of Euclidean spaces.
Singularities, double points, controlled topology and chain duality.
Singularities II: Automorphisms of Forms.
Singularities in contact geometry
In the first half of the paper, we consider singularities of infinitesimal contact transformations and first order partial differential equations, the main results being related to the classical Sternberg-Chen theorem for hyperbolic germs of vector fields. The second half explains how to construct global generating phase functions for solutions of Hamilton-Jacobi equations and see what their singularities look like.
Singularities in drawings of singular surfaces
When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and the singularities...
Singularities of implicit differential systems and maximum principle
The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding...
Singularities of implicit differential systems and their integrability
Singularities of k-tuples of vector fields [Book]
Singularities of nets of quadrics
Singularities of non-degenerate n-ruled (n + 1)-manifolds in Euclidean space
The objective of this paper is to study singularities of n-ruled (n + 1)-manifolds in Euclidean space. They are one-parameter families of n-dimensional affine subspaces in Euclidean space. After defining a non-degenerate n-ruled (n + 1)-manifold we will give a necessary and sufficient condition for such a map germ to be right-left equivalent to the cross cap × interval. The behavior of a generic n-ruled (n + 1)-manifold is also discussed.
Singularity theory and the geometry of a nonlinear elliptic equation
Slice Knots and Property R.
Smooth affine varieties and complete intersections.