Symplectic Energy and Lagrangian Intersection Under Legendrian Deformations

2007/05/20 by Her, Hai-Long
#53D10 #53D40 #57R22 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0705.2884

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 Z₂-Betti numbers of L, provided they intersect transversally.

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