The prism manifold realization problem III

The prism manifold realization problem II

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.

The prism manifold realization problem

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in $S^3$. 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 $S^3$ when $q<0$. The methodology undertaken to obtain…

棱柱quandle $P_7$ 在标准四维球面中的纤维实现

Fibred realizations of the prism quandle $P_7$ in the standard four-sphere

本文证明由四元数棱柱流形构造的两个同伦四维球面均为标准，并给出棱柱quandle阶五十六的两个不等价纤维实现，解决了阶七情形。

Knots with Prism Manifold Surgeries

Ballinger et al. have determined the list of all prism manifolds that are possibly realizable by Dehn surgeries on knots in $S^3$. In this paper, we explicitly find braid words of primitive/Seifert-fibered knots on which surface slope surgeries yield all the prism manifolds listed above. This completes the solution to the prism manifold realization problem.