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arxiv: 1206.2676 · v1 · pith:HYFWHQ72new · submitted 2012-06-12 · 🧮 math.SG

On the topology of monotone Lagrangian submanifolds

classification 🧮 math.SG
keywords lagrangianmonotoneadmitembeddingssomesubmanifoldstopologyconnected
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We find new obstructions on the topology of monotone Lagrangian submanifolds of $C^{n}$ under some hypothesis on the homology of their universal cover. In particular we show that nontrivial connected sums of manifolds of odd dimensions do not admit monotone Lagrangian embeddings into $\C^{n}$ whereas some of these examples are known to admit usual Lagrangian embeddings. In dimension three we get as a corollary that the only orientable Lagrangians in ${\bf C}^{3}$ are products $S^{1}\times \Sigma$.

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