Lagrangian Intersections, 3-Manifolds with Boundary, and the Atiyah-Floer Conjecture

Dietmar Salamon
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Dietmar Salamon: University of Warwick, Mathematics Institute

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 526-536 from Springer

Abstract: Abstract It has been observed by physicists for a long time that symplectic structures arise naturally from boundary value problems. For example, the Robbin quotient $$V = {\text{dom}}D*/{\text{dom}}D,$$ V = dom D * / dom D , associated to a symmetric (but not self-adjoint) operator D: dom D → H on a Hilbert space H carries a symplectic structure $$\omega (\upsilon ,\omega ) = \left\langle {D*\upsilon ,\left. \omega \right\rangle - \left\langle {\upsilon ,D*\omega } \right\rangle } \right.$$ ω ( υ , ω ) = 〈 D * υ , ω 〉 − 〈 υ , D * ω 〉 .

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_46

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