Topology Seminar (Main Talk): The prism manifold realization problem

Seminar | September 13 | 4-5 p.m. | 3 Evans Hall

 Faramarz Vafaee, Caltech

 Department of Mathematics

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in the three-sphere. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as \(P(p, q)\), for a pair of relatively prime integers \(p > 1\) and \(q\). We determine a complete list of prism manifolds \(P(p, q)\) that can be realized by positive integral surgeries on knots in the three-sphere. The methodology undertaken to obtain the classification relies on tools from Floer homology and lattice theory, and is primarily combinatorial in nature. This is joint work with Ballinger, Ni, and Ochse.