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Families of functions dominated by distributions of C -classes of mappings

Goo Ishikawa (1983)

Annales de l'institut Fourier

A subsheaf of the sheaf Ω of germs C functions over an open subset Ω of R n is called a sheaf of sub C function. Comparing with the investigations of sheaves of ideals of Ω , we study the finite presentability of certain sheaves of sub C -rings. Especially we treat the sheaf defined by the distribution of Mather’s 𝒞 -classes of a C mapping.

Families of jacobian manifolds and characteristic classes of surface bundles. I

Shigeyuki Morita (1989)

Annales de l'institut Fourier

In our previous work we have defined the notion of characteristic classes of surface bundles, which are differentiable fibre bundles whose fibres are closed oriented surfaces. In this paper we derive new relations between these characteristic classes by considering a canonical embedding of a given surface bundle with cross section to its associated family of Jacobian manifolds. As a key technical step we determine the first cohomology group of the mapping class group of oriented surfaces with coefficients...

Fano manifolds of degree ten and EPW sextics

Atanas Iliev, Laurent Manivel (2011)

Annales scientifiques de l'École Normale Supérieure

O’Grady showed that certain special sextics in 5 called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.

Fatgraph models of RNA structure

Fenix Huang, Christian Reidys, Reza Rezazadegan (2017)

Molecular Based Mathematical Biology

In this review paper we discuss fatgraphs as a conceptual framework for RNA structures. We discuss various notions of coarse-grained RNA structures and relate them to fatgraphs.We motivate and discuss the main intuition behind the fatgraph model and showcase its applicability to canonical as well as noncanonical base pairs. Recent discoveries regarding novel recursions of pseudoknotted (pk) configurations as well as their translation into context-free grammars for pk-structures are discussed. This...

Feuilles non captées et feuilles denses

Claude Lamoureux (1975)

Annales de l'institut Fourier

Nous démontrons une condition suffisante pour qu’une feuille non captée F d’un feuilletage t r . C 2 de codimension 1 soit dense.Cette condition n’exige aucune hypothèse de compacité ; de plus elle est souvent nécessaire.Dans le cas particulier d’un feuilletage par des feuilles simplement connexes elle s’énonce ainsi : le sécant d’homotopie de F contient un sous-semi-groupe abélien de rang 2.

Feuilletage canonique sur le fibré de Weil

Basile Guy Richard Bossoto (2010)

Colloquium Mathematicae

Let be M a smooth manifold, A a local algebra and M A a manifold of infinitely near points on M of kind A. We build the canonical foliation on M A and we show that the canonical foliation on the tangent bundle TM is the foliation defined by its canonical field.

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