Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations

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Her, Hai-Long
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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.
Comment: 16 pages, to appear in the Pacific Journal of Mathematics
Keywords
Mathematics - Symplectic Geometry, 53D10, 53D40, 57R22
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