Topologie de Gromov équivariante, structures hyperboliques et arbres réels.
Topologie des fonctions régulières et cycles évanescents.
One has two notions of vanishing cycles: the Deligne's general notion and a concrete one used recently in the study of polynomial functions. We compare these two notions which gives us in particular a relative connectivity result. We finish with an example of vanishing cycle calculation which shows the difficulty of a good choice of compactification.
Topologie des hypersurfaces pfaffiennes
Topologie d'un polynôme de deux variables complexes au voisinage de l'infini
Nous donnons un système complet d’invariants de la classe de conjugaison topologique de polynômes de en dehors d’un compact suffisamment grand dans les deux sens suivants : en tant que feuilletages (en oubliant les valeurs des fibres) et en tant que fonctions. Ces invariants sont donnés par un arbre pondéré, fléché et coloré, obtenu à partir de la résolution des singularités du polynôme sur la droite à l’infini. Nous donnons un critère de régularité pour les valeurs d’un polynôme et une description...
Topologie symplectique, convexité holomorphe et structures de contact
Topologien auf Schnittmoduln kohärenter komplex- und reell-analytischer Garben.
Topologies defined by some invariant pseudodistances
Topologies semi-vectorielles. Application à l'analyse complexe
On définit sur un espace vectoriel une classe de topologies qui rendent la multiplication continue, mais ne sont pas vectorielles en général. Sur un espace complexe elles permettent d’obtenir encore les principales propriétés des fonctions plurisousharmoniques. De telles topologies séparées sont localement pseudo-convexes (mais non localement convexes en général) : cette notion intervient dans les extensions données récemment par l’auteur du théorème de Banach-Steinhaus aux familles de polynômes...
Topologisch triviale holomorphe Vektorbündel auf ... (...).
Topologische Fortsetzung biholomorpher Funktionen auf dem Rande bei beschränkten streng-pseudokonvexen Gebieten im Cn mit C°°- Rand.
Topologische globale Moduln.
Topology and geometry of caustics in relation with experiments
Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We...
Topology of arrangements and position of singularities
This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...
Topology of families of affine plane curves
We determine bifurcation sets of families of affine curves and study the topology of such families.
Topology of Fatou components for endomorphisms of : linking with the Green’s current
Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms , when k >1. Classical theory describes U(f) as the complement in of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on , we give a definition of linking number between closed loops in and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in . As an application, we use these linking...
Torelli theorems for Kähler K3 surfaces
Torelli theorems for singularieties (Erratum).
Torelli theorems for singularities.
Toric embedded resolutions of quasi-ordinary hypersurface singularities
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is...
Toroidal Degeneration of Abelian Varieties. II.