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Almost holomorphic embeddings in Grassmannians with applications to singular symplectic submanifolds
In this paper we use Donaldson's approximately holomorphic techniques to build embeddings of a closed symplectic manifold with symplectic form of integer class in the Grassmannians Gr(r, N). We assure that these embeddings are asymptotically hol[...]texto impreso
This paper discusses the construction of asymptotically holomorphic embeddings of a (2n?1) -dimensional contact manifold into the projective space CP 2n+1 such that the image is weakly dominated by the symplectic form. The proof follows the s[...]texto impreso
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.texto impreso
Fernández Fuertes, Eduardo ; Martínez-Aguinaga, Javier ; Presas, Francisco | Mathematical Sciences Publishers (MSP) | 2020We compute the fundamental group of each connected component of the space of formal Legendrian embeddings in R3. We use it to show that previous examples in the literature of nontrivial loops of Legendrian embeddings are already nontrivial at th[...]texto impreso
We prove that the vanishing spheres of the Lefschetz pen- cils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplec- tomorphism group of the fiber. More precisely, a number of generaliz[...]texto impreso
Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifol[...]texto impreso
A contact form on a (2n+1) -dimensional differential manifold M is a 1 -form ? such that ??(d?) n is a volume form; the hyperplane field ?=ker? is the associated (co-oriented) contact structure. A contact form induces a reduction of the str[...]
