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

By M. Damian. 2010

52 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7d5431add584889dad64b8c1f283d11cb0ee4bb5

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Generating the Fukaya categories of Hamiltonian 𝐺-manifolds (2015, background): “le on L is a k-tuple {E i,i+1} k−1 i=0 of ﬂat 2One could also use higher rank local systems, as in [3], but this can cause issues in the presence of Maslov 2 discs, as exploited in the work of Damian [19]; see [38] for a fuller discussion of these issues. Generating the Fukaya categories of Hamilton”
Punctured holomorphic curves and Lagrangian embeddings (2014, background): “bo [57] and Polterovich [54], in the monotone case for n ≤ 24 by Oh [52], and in the monotone case for general n by Buhovsky [12] and by Fukaya, Oh, Ohta and Ono [28, Theorem 6.4.35], see also Damian [22]. A diﬀerent approach has been outlined by Fukaya [27]. The scheme to prove Audin’s conjecture u”