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Feuilletages des surfaces

Gilbert Levitt (1982)

Annales de l'institut Fourier

On étudie, sur les surfaces compactes orientables, les feuilletages orientables (i.e. pouvant être définis par un champ de vecteurs) dont les singularités sont des selles. Ces feuilletages sont considérés modulo isotopies et opérations de Whitehead préservant l’orientabilité du feuilletage. Dans le première partie on définit les “feuilletages connexes”, ceux pour lesquels par deux points quelconques passe une transversable fermée. De façon équivalente, le feuilletage est la suspension d’un échange...

Feuilletages holomorphes de codimension un dont la classe canonique est triviale

Frédéric Touzet (2008)

Annales scientifiques de l'École Normale Supérieure

We give a description of Kähler manifolds M equipped with an integrable subbundle ℱ of T M of rank n - 1 ( n = dim M ) under the assumption that the line bundle D é t ℱ is numerically trivial. This is a sort of foliated version of Bogomolov’s theorem concerning Kähler manifolds with trivial canonical class.

Fiber product preserving bundle functors as modified vertical Weil functors

Włodzimierz M. Mikulski (2015)

Czechoslovak Mathematical Journal

We introduce the concept of modified vertical Weil functors on the category ℱ ℳ m of fibred manifolds with m -dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on ℱ ℳ m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil...

Fiber product preserving bundle functors on all morphisms of fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of r -jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.

Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok (2000)

Annales de l'institut Fourier

We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H 1 ( G a m m a , Φ ) ≠ 0 for some unitary representation Φ . By our earlier work there exists a d -closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ' , possibly non-isomorphic to Φ . Taking norms we obtains a positive...

Final forms for a three-dimensional vector field under blowing-up

Felipe Cano (1987)

Annales de l'institut Fourier

We study the final situations which may be obtained for a singular vector field by permissible blowing-ups of the ambient space (in dimension three). These situations are preserved by permissible blowing-ups and its structure is simple from the view-point of the integral branches. Technically, we take a logarithmic approach, by marking in each step the exceptional divisor of the transformation.

Finding linking sets.

Schechter, Martin, Tintarev, Kyril (2006)

International Journal of Mathematics and Mathematical Sciences

Finite closed coverings of compact quantum spaces

Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński (2012)

Banach Center Publications

We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space ℙ ∞ the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...

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