The realization problem of prism manifolds
Prism manifolds are spherical 3-manifolds with D-type finite fundamental groups. They can be parametrized by a pair of relatively prime integers p>1 and q. The realization problem of prism manifolds asks which prism manifolds can be obtained by positive Dehn surgery on a knot in S3. We will discuss the basic idea of the solution of the realization problem. This talk is based on joint work with (subsets of) Ballinger, Hsu, Mackey, Ochse and Vafaee.