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- handle: 10670/1.pdlogd
- doi: 10.60527/3q7e-9t71
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François Lalonde, « François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 1) », Canal-U, la vidéothèque de l'enseignement supérieur, ID : 10.60527/3q7e-9t71
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The first two lectures will present the fundamental results of symplectic topology : basic definitions, Moser’s lemma, normal forms of the symplectic structure near symplectic and Lagrangian submanifolds, characterization of Hamiltonian fibrations over any CW-complex. The third course will give the application of quantum homology to the splitting of the rational cohomology ring of any Hamiltonian fibration over S2, a generalization of a result of Deligne in the algebraic case and of Kirwan in the toric case. The fourth course will give the application of the quantum homology of a Lagrangian submanifold to the proof of the triviality of the monodromy of a weakly exact Lagrangian submanifold in any symplectic manifold.