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# Mathematical Research Letters

## Volume 21 (2014)

### Number 1

### Topologically distinct Lagrangian and symplectic fillings

Pages: 85 – 99

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n1.a7

#### Authors

#### Abstract

We construct infinitely many Legendrian links in the standard contact $\mathbb{R}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces of algebraic curves in $B^4 \subset \mathbb{C}^2$, is applied to find contact $3$-manifolds with topologically distinct symplectic fillings, and is generalized to higher dimensions.

#### 2010 Mathematics Subject Classification

53D12, 57R17