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arXiv · 1206.2676

On the topology of monotone Lagrangian submanifolds

Mihai Damian
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Abstract

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 $S^{1}\times Σ$.

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Mihai Damian. 2012-06-12. On the topology of monotone Lagrangian submanifolds. https://arxiv.org/abs/1206.2676

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