Communications in Analysis and Geometry

Volume 29 (2021)

Number 6

The prism manifold realization problem II

Pages: 1279 – 1334



William Ballinger (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

Yi Ni (Department of Mathematics, California Institute of Technology, Pasadena, Calif., U.S.A.)

Tynan Ochse (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)

Faramarz Vafaee (Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)


We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers $p \gt 1$ and $q$. We determine a complete list of prism manifolds $P(p, q)$ that can be realized by positive integral surgeries on knots in $S^3$ when $q \gt p$. The methodology undertaken to obtain the classification is similar to that of the case $q \lt 0$ in an earlier paper.

Received 4 May 2018

Accepted 17 December 2018

Published 11 January 2022