Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations
Symplectic Geometry
2007-05-23 v1
Abstract
Let M be a compact symplectic manifold, and L be a closed Lagrangian submanifold which can be lifted to a Legendrian submanifold in the contactization of M. For any Legendrian deformation of L satisfying some given conditions, we get a new Lagrangian submanifold L'. We prove that the number of intersection of L and L' can be estimated from below by the sum of -Betti numbers of L, provided they intersect transversally.
Cite
@article{arxiv.0705.2884,
title = {Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations},
author = {Hai-Long Her},
journal= {arXiv preprint arXiv:0705.2884},
year = {2007}
}