Remarks on monotone Lagrangians in $\mathbf{C}^n$
Abstract
We derive some restrictions on the topology of a monotone Lagrangian submanifold $L\subset\mathbf{C}^n$ by making observations about the topology of the moduli space of Maslov 2 holomorphic discs with boundary on $L$ and then using Damian's theorem which gives conditions under which the evaluation map from this moduli space to $L$ has nonzero degree. In particular we prove that an orientable 3manifold admits a monotone Lagrangian embedding in $\mathbf{C}^3$ only if it is a product, which is a variation on a theorem of Fukaya. Finally we prove an hprinciple for monotone Lagrangian immersions.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.0927
 Bibcode:
 2011arXiv1110.0927E
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Differential Geometry;
 53D12;
 53D40
 EPrint:
 10 pages + 1 page corrigendum (correcting the statement and proof of Proposition 12)