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Exact Lagrangian submanifolds in simply-connected cotangent bundles

Kenji Fukaya·Paul Seidel·Ivan Smith
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Abstract

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.

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Kenji Fukaya, Paul Seidel, Ivan Smith. 2007-01-26. Exact Lagrangian submanifolds in simply-connected cotangent bundles. https://doi.org/10.1007/s00222-007-0092-8

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