Regular Lagrangians are smooth Lagrangians
Copyright policy )Regular Lagrangians are smooth Lagrangians
We prove that for any element in the $γ$-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its $γ$-support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the $γ$-support of an element in the completion is compact, then it is connected.
16 pages, 2 figures. v2: Revised, to appear in J. Math. Soc. Japan
Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Algebraic Topology (math.AT), Mathematics - Category Theory, Category Theory (math.CT), Mathematics - Algebraic Topology, 53D12, 37J11, 35A27
Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Algebraic Topology (math.AT), Mathematics - Category Theory, Category Theory (math.CT), Mathematics - Algebraic Topology, 53D12, 37J11, 35A27
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