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

Abstract

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 ${\mathbf{C}}^{\mathbf{n}}$, 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.

to appear in Comment. Math. Helvetici

References in corpus (4)

• Quantum Structures for Lagrangian Submanifolds
• Microlocal branes are constructible sheaves
• The symplectic geometry of cotangent bundles from a categorical viewpoint
• Constraints on exact Lagrangians in cotangent bundles of manifolds fibred over the circle