Lagrangian embeddings into subcritical Stein manifolds

By P. Biran, Kai Cieliebak. 2002

52 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ad705149bac309d86c992e57a23031d01c451bf5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. M. Abouzaid
2. Urs Frauenfelder
3. I. Smith
4. Klaus Mohnke
5. O. Cornea
6. P. Seidel
7. Kai Cieliebak
8. P. Biran

In Geometry and Topology

1. M. Abouzaid
2. A. Oancea
3. P. Seidel
4. Kai Cieliebak
5. I. Smith
6. Alexander F. Ritter
7. Urs Frauenfelder
8. Frederick J. Bourgeois III

Citations in the corpus

• Rigidity and uniruling for Lagrangian submanifolds (2008, background): “See also Eliashberg and Gromov [28] and Eliashberg [27] for the foundations of symplectic geometry of Stein manifolds, as well as Biran and Cieliebak [10; 9] and Biran [8] for applications of these concepts to questions on Lagrangian submanifolds.”
• A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS (2007, background): “7 generalizes (for spheres) the well-known result [24, 1, 3] that there exist no exact Lagrangian embeddings into subcritical Stein manifolds.”
• Applications of Hofer's geometry to Hamiltonian dynamics (2003, background): “For (ii) we follow [1, 3]: Let S ⊂ k+1 be the unit sphere, and let ωSF be the Study–Fubini form on P normalized so that the pull-back of ωSF by the Hopf fibration h : S → P is equal to the restriction of the standard form ω0 on .”
• Holomorphic Disks and the Chord Conjecture (2000, methodology): “We have not answered Arnold’s original question yet, whether there always exists a Reeb orbit intersecting the Legendrian submanifold at least twice.”
• Rabinowitz Floer homology and symplectic homology (2009, background): “The proof given above only uses the fact that the subcritical skeleton can be displaced from itself [3].”
• Lagrangian non-intersections (2004, background): “See [8] for more details on this type of argument.”
• Framed bordism and Lagrangian embeddings of exotic spheres (2008, methodology): “The analytic ingredients are gluing theorems, and our approach follows as closely as possible the one used in Fukaya, Oh, Ohta, and Ono’s book [9]; the only significant difference is that they use obstruction bundles to reduce their gluing theorem to one where all marked points are fixed.”
• THE SYMPLECTIC TOPOLOGY OF RAMANUJAM'S SURFACE (2004, background): “Ramanujam showed in [21] that the complementM of a certain singular curve in the Hirzebruch surface F1 is a contractible algebraic surface.”