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.
Original language | English |
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Pages (from-to) | 1241-1255 |
Number of pages | 15 |
Journal | Mathematical Research Letters |
Volume | 21 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 |