The structure of the cut locus in dimension less than or equal to six
The topology of integrable differential forms near a singularity
The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3
The versality discriminant and local topological equivalence of mappings
We will extend the infinitesimal criteria for the equisingularity (i.e. topological triviality) of deformations of germs of mappings , , to non-finitely determined germs (these occur generically outside the “nice dimensions” for Mather, even among topologically stable mappings). The failure of finite determinacy is described geometrically by the “versality discriminant”, which is the set of points where is not stable (i.e. viewed as an unfolding it is not versal). The criterion asserts that...
Thom polynomials for open Whitney umbrellas of isotropic mappings
A smooth mapping of a smooth n-dimensional manifold L into a smooth 2n-dimensional symplectic manifold (M,ω) is called isotropic if f*ω vanishes. In the last ten years, the local theory of singularities of isotropic mappings has been rapidly developed by Arnol’d, Givental’ and several authors, while it seems that the global theory of their singularities has not been well studied except for the work of Givental’ [G1] in the case of dimension 2 (cf. [A], [Au], [I2], [I-O]). In the present paper,...
Topological Sufficiency of Smooth Map-Germs.
Topological Triviality of Deformations of Functions and Newton Filtrations.
Topological triviality of versal unfoldings of complete intersections
We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.The algebraic conditions are related to the operation of adjoining powers,...
Topological Type in Families of Germs.
Transversalities for Lagrange singularities of isotropic mappings of corank one
Travaux de Thom sur les singularités
Travaux d'Ecalle et de Martinet-Ramis sur les systèmes dynamiques
Unfoldings in Knot Theory.
Unfoldings Knot Theory (Corrigendum).
Unfoldings of foliations with multiform first integrals
Let be a codim 1 local foliation generated by a germ of the form for some complex numbers and germs of holomorphic functions at the origin in . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for is equivalent to the unfolding theory for the multiform function...
Unfoldings of Meromorphic Functions.
Unique Normal Forms for Planar Vector Fields.
Universal Families of C°°-Functions on D2.
Universal topological stratification for the Pham example
Universelle Familien differenzierbarer Funktionen auf der Kreislinie.