The prism manifold realization problem II

TL;DR

This paper classifies which prism manifolds can be obtained by positive integral surgeries on knots in the 3-sphere, focusing on the case where the parameter q exceeds p, extending previous work on the q<0 case.

Contribution

It provides a complete list of realizable prism manifolds P(p, q) via positive surgeries for q>p, advancing the understanding of the realization problem for these manifolds.

Findings

Complete classification of prism manifolds realizable by positive surgeries with q>p

Extension of previous classification methods to new parameter range

Identification of all such manifolds in the specified case

Abstract

We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers $p>1$ 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 $q>p$. The methodology undertaken to obtain the classification is similar to that of the case $q<0$ in an earlier paper.