Knots with Prism Manifold Surgeries

TL;DR

This paper explicitly finds braid words for primitive/Seifert-fibered knots that produce all prism manifolds via surface slope surgeries, completing the realization problem for these manifolds.

Contribution

It provides explicit braid words for knots that realize all prism manifolds through surface slope surgeries, solving the prism manifold realization problem.

Findings

Explicit braid words for primitive/Seifert-fibered knots identified

All listed prism manifolds realized by these knots

Completes the classification of prism manifolds from knot surgeries

Abstract

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.