The prism manifold realization problem III

Abstract

Every prism manifold can be parametrized by a pair of relatively prime integers p > 1 $p>1$ and q $q$ . In our earlier papers, we determined a complete list of prism manifolds P ( p , q ) $P(p, q)$ that can be realized by positive integral surgeries on knots in S 3 $S^3$ when q < 0 $q<0$ or q > p $q>p$ ; in the present work, we solve the case when 0 < q < p $0<q<p$ . This completes the solution of the realization problem for prism manifolds.