Mathematical Research Letters

Volume 21 (2014)

Number 1

Topologically distinct Lagrangian and symplectic fillings

Pages: 85 – 99



Chang Cao (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Nathaniel Gallup (Department of Mathematics, University of California at Davis)

Kyle Hayden (Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, U.S.A.)

Joshua M. Sabloff (Department of Mathematics and Statistics, Haverford College, Haverford, Pennsylvania, U.S.A.)


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

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