Symplectic energy and Lagrangian intersection under Legendrian deformations
Hai-Long Her
May 20, 2007
Citations
4
Citations
Journal
Pacific Journal of Mathematics
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Semantic Scholar
Key Takeaway Key Takeaway: The number of intersections between L and L' can be estimated from below by the sum of $Z_2$-Betti numbers of L, provided they intersect transversally.
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 $Z_2$-Betti numbers of L, provided they intersect transversally.
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