arXiv subjects
Publications and source records attributed to Dong Heon Choe.
We give a complete classification of the spherical 3-manifolds that bound smooth rational homology 4-balls. Furthermore, we determine the order of spherical 3-manifolds in the rational homology cobordism group of rational homology 3-spheres. To this end, we use constraints for 3-manifolds to bound rational homology balls induced from Donaldson's diagonalization theorem and Heegaard Floer correction terms.
We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by $Y$. To this end, we make use of constraints on definite forms bounded by $Y$ induced from Donaldson's diagonalization theorem, and correction term invariants due to Frøyshov, and Ozsváth and Szabó. In particular, we prove that all spherical 3-manifolds satisfy such finiteness property.