Symplectic rational homology ball fillings of Seifert fibered spaces
Joint work with Burak Ozbagci and Bulent Tosun,
Preprint 2024

We characterize when some small Seifert fibered spaces can be the convex boundary of a symplectic rational homology ball and give strong restrictions for others to bound such manifolds. As part of this we show that the only spherical $3$-manifolds that are the boundary of a symplectic rational homology ball are the lens spaces $L(p^2,pq-1)$ found by Lisca and give evidence for the Gompf conjecture that Brieskorn spheres do not bound Stein domains in $\C^2$. We also find restrictions on Lagrangian disk fillings of some Legendrian knots in small Seifert fibered spaces.

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