Symplectic energy and Lagrangian intersection under Legendrian deformations

Hai-Long Her
2007 Pacific Journal of Mathematics  
Let M be a compact symplectic manifold, and L ⊂ M 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 L ∩ L can be estimated from below by the sum of ‫ޚ‬ 2 -Betti numbers of L, provided they intersect transversally. MSC2000: 57R22, 53D40, 53D12, 53D10.
doi:10.2140/pjm.2007.231.417 fatcat:jvjnakl5tjhtnaf4ewdg55btd4