On the topology of monotone Lagrangian submanifolds

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 ${\mathbf{C}}^3$ are products $S^1\times \Sigma$.