### Abstract

Original language | English |
---|---|

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

*Mathematical Research Letters*,

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

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

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 21, no. 6, pp. 1241-1255. https://doi.org/10.4310/MRL.2014.v21.n6.a2

}

TY - JOUR

T1 - Remarks on monotone Lagrangians in C^n

AU - Evans, Jonathan David

AU - Kedra, Jarek

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.4310/MRL.2014.v21.n6.a2

DO - 10.4310/MRL.2014.v21.n6.a2

M3 - Article

VL - 21

SP - 1241

EP - 1255

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 6

ER -