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Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry–Mather theory
Published online by Cambridge University Press: 31 August 2017
Abstract
We construct graph selectors for compact exact Lagrangians in the cotangent bundle of an orientable, closed manifold. The construction combines Lagrangian spectral invariants, developed by Oh, and results, by Abouzaid, about the Fukaya category of a cotangent bundle. We also introduce the notion of Lipschitz-exact Lagrangians and prove that these admit an appropriate generalisation of graph selector. We then, following Bernard–Oliveira dos Santos, use these results to give a new characterisation of the Aubry and Mañé sets of a Tonelli Hamiltonian and to generalise a result of Arnaud on Lagrangians invariant under the flow of such Hamiltonians.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 3 , November 2018 , pp. 411 - 434
- Copyright
- Copyright © Cambridge Philosophical Society 2017
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