# Remarks on monotone Lagrangians in $\mathbf{C}^n$

@article{Evans2011RemarksOM, title={Remarks on monotone Lagrangians in \$\mathbf\{C\}^n\$}, author={Jonathan D. Evans and Jarek Kcedra}, journal={arXiv: Symplectic Geometry}, year={2011} }

We derive some restrictions on the topology of a monotone Lagrangian submanifold $L\subset\mathbf{C}^n$ 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 $\mathbf{C}^3$ only if it is a product, which is a…

## 6 Citations

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Let $\mathcal{N}$ be the total space of a bundle over some $k$-dimensional torus with fibre $\mathcal{R}$, where $\mathcal{R}$ is diffeomorphic to $S^k \times S^l$, or $S^k \times S^l \times S^m$, or…

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We present techniques, inspired by monodromy considerations, for constructing compact monotone Lagrangians in certain affine hypersurfaces, chiefly of Brieskorn–Pham type. We focus on dimensions 2…

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Let L be a Lagrangian submanifold in a symplectic vector space which is closed, oriented and spin. Using virtual fundamental chains of moduli spaces of nonconstant pseudo‐holomorphic disks with…

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Abstract The width of a Lagrangian is the largest capacity of a ball that can be symplectically embedded into the ambient manifold such that the ball intersects the Lagrangian exactly along the real…

### Fukaya's work on Lagrangian embeddings

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This is an expository account of some applications of string topology to the study of Lagrangian embeddings into symplectic manifolds, originally due to Fukaya, which was written as a contribution to…

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