Loops of Lagrangian submanifolds and pseudoholomorphic discs

By Meike Akveld, Dietmar Salamon. 2000

52 citations recorded by the source corpus.

Abstract. We examine three invariants of exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Polterovich for loops of Hamiltonian symplectomorphisms. One of these is the minimal Hofer length in a given Hamiltonian isotopy class. We determine the exact values of these invariants for loops of projective Lagrangian planes. The proof uses the Gromov invariants of an associated symplectic fibration over the 2-disc with a Lagrangian subbundle over the boundary.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/41071f955a8ab12f2fe3b57db3822c85ed83ae0e

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In Applied Mathematics

1. O. Cornea
2. P. Biran
3. Urs Frauenfelder
4. I. Smith
5. Cheol-Hyun Cho
6. M. Abouzaid
7. E. Shelukhin
8. A. Kislev

In Geometry and Topology

1. O. Cornea
2. P. Biran
3. P. Seidel
4. I. Smith
5. Urs Frauenfelder
6. L. Polterovich
7. F. Schlenk
8. Kai Cieliebak

Citations in the corpus

• On Continuity of Quasimorphisms for Symplectic Maps (2012, unknown): “The partition of A+ into squares can be chosen so that it extends a partition of J × [1,2] ⊂ A+ into squares of the same size.”
• Quantum Structures for Lagrangian Submanifolds (2007, background): “A simple calculation (see [44, 3]) shows that if κ > RH(s, t, x) for every (s, t, x) ∈ D ×M then ω̃H,κ is symplectic.”