English

On the topology of monotone Lagrangian submanifolds

Symplectic Geometry 2012-06-14 v1

Abstract

We find new obstructions on the topology of monotone Lagrangian submanifolds of CnC^{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 \Cn\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 C3{\bf C}^{3} are products S1×ΣS^{1}\times \Sigma.

Keywords

Cite

@article{arxiv.1206.2676,
  title  = {On the topology of monotone Lagrangian submanifolds},
  author = {Mihai Damian},
  journal= {arXiv preprint arXiv:1206.2676},
  year   = {2012}
}