Remarks on monotone Lagrangians in C^n

Jonathan David Evans, Jarek Kedra

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1241-1255
Number of pages15
JournalMathematical Research Letters
Volume21
Issue number6
DOIs
Publication statusPublished - 2014

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Monotone
Moduli Space
H-principle
Topology
Lagrangian Submanifold
Immersion
Theorem
Restriction
Evaluation
Observation

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Remarks on monotone Lagrangians in C^n. / Evans, Jonathan David; Kedra, Jarek.

In: Mathematical Research Letters, Vol. 21, No. 6, 2014, p. 1241-1255.

Research output: Contribution to journalArticle

Evans, Jonathan David ; Kedra, Jarek. / Remarks on monotone Lagrangians in C^n. In: Mathematical Research Letters. 2014 ; Vol. 21, No. 6. pp. 1241-1255.
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