Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations

Details Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations

2007-05-20

arxiv.org/abs/0705.2884v1

Mathematics

Symplectic Geometry

16 pages, to appear in the Pacific Journal of Mathematics

Scientific paper

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 $Z_2$-Betti numbers of L, provided they intersect transversally.

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