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Remarks on monotone Lagrangians in Cn

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>2/04/2015
<mark>Journal</mark>Mathematical Research Letters
Issue number6
Volume21
Number of pages15
Pages (from-to)1241-1255
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We derive some restrictions on the topology of a monotone Lagrangian submanifold ⊂ 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.