Lagrangian intersections, 3-manifolds with boundary, and the Atiyah-Floer conjecture
نویسنده
چکیده
Self-adjoint extensions of D correspond to Lagrangian subspaces of V and, moreover, the kernel of D determines such a Lagrangian subspace whenever D has a closed range. IfD is a symmetric differential operator on a manifold with boundary then, by partial integration, the form ω is given by an integral over the boundary. For example, if D is the Hessian of the symplectic action functional on paths in R, then the space V = R × R corresponds to the two boundary values of the path and the symplectic structure is (−ω0) ⊕ ω0 where ω0 = ∑
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