The analytic Carathéodory conjecture.
The chess conjecture.
The directional dimension of subanalytic sets is invariant under bi-Lipschitz homeomorphisms
Let be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at .Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and are also subanalytic. In particular if two subanalytic...
The Geometry of Critical and Near-Critical Values of Differentiable Mappings.
The index of analytic vector fields and Newton polyhedra
We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic vector fields....
The Intersection Matrix of Brieskorn Singularities.
The L²-invariants and Morse numbers
We study the homotopy invariants of free cochain complexes and Hilbert complexes. These invariants are applied to calculation of exact values of Morse numbers of smooth manifolds.
The link of an extrovert divide
The linking number of singular maps.
The Monodromy of a Curve with Ordinary Double Points.
The multiplicity of the Lyashko-Looijenga mapping on the discriminant strata of even and odd polynomials
The Signature of Milnor Fibres and Duality Theorem for Strongly Pseudoconvex Manifolds.
The structure of the cut locus in dimension less than or equal to six
Théorème de Kuiper—Kuo—Bochnak—Lojasiewicz à l'infini
Thom polynomials and Schur functions: the singularities
We give the Thom polynomials for the singularities associated with maps with parameter . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.
Thom polynomials and Schur functions: the singularities
We give a closed formula for the Thom polynomials of the singularities in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.
Topological Triviality of Deformations of Functions and Newton Filtrations.
Topological Type in Families of Germs.
Toward a general theory of linking invariants.
Travaux de Thom sur les singularités