Remarks on monotone Lagrangians in C^n

Jonathan David Evans, Jarek Kedra

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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 1241-1255 15 Mathematical Research Letters 21 6 https://doi.org/10.4310/MRL.2014.v21.n6.a2 Published - 2014