Remarks on monotone Lagrangians in $\CC^n$

Details Remarks on monotone Lagrangians in $\CC^n$ Remarks on monotone Lagrangians in $\CC^n$

2011-10-05

arxiv.org/abs/1110.0927v2

Mathematics

Symplectic Geometry

6 pages; Section 4.2 added

Scientific paper

We derive some restrictions on the topology of a monotone Lagrangian submanifold $L\subset\CC^n$ 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 3-manifold admits a monotone Lagrangian embedding in $\CC^3$ 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.

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