Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Remarks on monotone Lagrangians in Cn
AU - Evans, Jonathan David
AU - Kedra, Jarek
PY - 2015/4/2
Y1 - 2015/4/2
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 - Journal article
VL - 21
SP - 1241
EP - 1255
JO - Mathematical Research Letters
JF - Mathematical Research Letters
SN - 1073-2780
IS - 6
ER -