Symplectic fillings, contact surgeries, and Lagrangian disks
Joint work with James Conway and Bulent Tosun,
IMRN 2021 no.~8 (2021), 6020--6050.

This paper completely answers the question of when contact $(r)$--surgery on a Legendrian knot in the standard contact structure on $S^3$ yields a symplectically fillable contact manifold for $r\in(0,1]$. We also give obstructions for other positive $r$ and investigate Lagrangian fillings of Legendrian knots.

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