A note on codimension-1 foliations
A note on Donaldson polynomials for K3 surfaces.
A note on generalized flag structures
Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.
A note on octahedral spherical foldings.
A note on projective Levi flats and minimal sets of algebraic foliations
In this paper we prove that holomorphic codimension one singular foliations on have no non trivial minimal sets. We prove also that for , there is no real analytic Levi flat hypersurface in .
A Note on Right-Equivalence of Map-Germs.
A note on tangentially equivalent manifolds
A note on the Boardman theorem.
A note on the cohomology ring of the oriented Grassmann manifolds
We use known results on the characteristic rank of the canonical –plane bundle over the oriented Grassmann manifold to compute the generators of the –cohomology groups for . Drawing from the similarities of these examples with the general description of the cohomology rings of we conjecture some predictions.
A note on the height of the third Stiefel--Whitney class of the canonical vector bundles over some Grassmann manifolds
We compute the height of the third Stiefel--Whitney characteristic class of the canonical bundles over some infinite classes of Grassmann manifolds of five dimensional vector subspaces of real vector spaces.
A note on the local structure of levels of a plane vector field
A Note on the Rational Cuspidal Curves
In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
A note on trignometric sums arising in gauge theory.
A Periodic Flow with Infinite Epstein Hierarchy.
A proof of Reidemeister-Singer’s theorem by Cerf’s methods
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
A proof of the Chern-Lashof conjecture in dimensions greater than five.
A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.
À propos de l'existence de fibrés stables sur les surfaces.
À propos d'un théorème de Charles Ehresmann sur les feuilletages
A quadratic form on the quotient of a periodic map.