Nous construisons sur l’ensemble des feuilletages (avec singulariés) d’un espace analytique compact normal une structure analytique complexe. Dans le cas faiblement kählérien, nous montrons qu’à un point frontière de la compactification naturelle de l’espace des feuilletages est encore associé un feuilletage.
We give an example of a uniform quotient map from R2 to R which has non-locally connected level sets.
The main result is a Pursell-Shanks type theorem for codimension one foliations. This theorem can be viewed as a partial solution of a hypothetical general version of the theorem of Pursell-Shanks. Several propositions and lemmas on foliations are contained in the proof.
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup of finite index in Bₙ. For each equivalence class...
Let be a path on vertices. In an earlier paper we have proved that each polyhedral map on any compact -manifold with Euler characteristic contains a path such that each vertex of this path has, in , degree . Moreover, this bound is attained for or , even. In this paper we prove that for each odd , this bound is the best possible on infinitely many compact -manifolds, but on infinitely many other compact -manifolds the upper bound can be lowered to .