Remarks on monotone Lagrangians in Cn

Evans, Jonathan David and Kedra, Jarek (2015) Remarks on monotone Lagrangians in Cn. Mathematical Research Letters, 21 (6). pp. 1241-1255. ISSN 1073-2780

Abstract

We derive some restrictions on the topology of a monotone Lagrangian submanifold L ⊂ Cn 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 3-manifold admits a monotone Lagrangian embedding in C3 only if it is a product, which is a variation on a theorem of Fukaya. Finally, we prove an h-principle for monotone Lagrangian immersions.