Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds

Details Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds

2010-06-17

arxiv.org/abs/1006.3398v1

Mathematics

Symplectic Geometry

to appear in Comment. Math. Helvetici

Scientific paper

We establish a new version of Floer homology for monotone Lagrangian submanifolds and apply it to prove the following (generalized) version of Audin's conjecture : if $L$ is an aspherical manifold which admits a monotone Lagrangian embedding in ${\bf C^{n}}$, then its Maslov number equals $2$. We also prove other results on the topology of monotone Lagrangian submanifolds $L\subset M$ of maximal Maslov number under the hypothesis that they are displaceable through a Hamiltonian isotopy.

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