### 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 |

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## Cite this

Evans, J. D., & Kedra, J. (2014). Remarks on monotone Lagrangians in C^n.

*Mathematical Research Letters*,*21*(6), 1241-1255. https://doi.org/10.4310/MRL.2014.v21.n6.a2