2025/05/07 by John B. Etnyre, Etnyre, John B., Burak Özbağcı +3
Mathematics · Medicine · #Mathematics and Applications #Parkinson's Disease and Spinal Disorders
paper · pdf · doi:10.48550/arxiv.2505.04513
We show that a small Seifert fibered space with complementary legs does not symplectically bound a rational homology ball for at least one choice of orientation. In the case e0≤ -1, we characterize when a small Seifert fibered space with uniquely complementary legs symplectically bounds a rational homology ball. In the case e0≥ 0, we characterize when a small Seifert fibered space with complementary legs, equipped with a balanced contact structure, symplectically bounds a rational homology ball. Our results highlight a sharp contrast with the smooth category, where many more such Seifert fibered spaces are known to bound smooth rational homology balls. As a consequence of the results above, we also complete the classification of contact structures on oriented spherical 3-manifolds that admit symplectic rational homology ball fillings. In particular, we show that a closed, oriented 3-manifold with finite fundamental group admits at most six contact structures, up to isotopy, which are symplectically fillable by rational homology balls.