ON THE TOPOLOGY OF MONOTONE LAGRANGIAN SUBMANIFOLDS

We find new obstructions on the topology of closed monotone Lagrangian submanifolds of C-n under some hypotheses 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: the question of the existence of a monotone embedding for a given Lagrangian in C-n was open. In dimension three we get as a corollary that the only orientable Lagrangians in C-3 are products S-1 x Sigma. The main ingredient of our proofs is the lifted Floer homology theory which we developed in [13].