Knots with Prism Manifold Surgeries

2019/09/05 by Zhengyuan Shang, Shang, Zhengyuan
Dentistry · Mathematics · Medicine · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Orthodontics and Dentofacial Orthopedics #Orthopedic Surgery and Rehabilitation

paper · pdf · doi:10.48550/arxiv.1909.02252

openalex publication_date 2019/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ballinger et al. have determined the list of all prism manifolds that are possibly realizable by Dehn surgeries on knots in S³. 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.

Citations

• Integral Finite Surgeries on Knots in S³
• Modifications and Cobounding Manifolds

Related

• The prism manifold realization problem II
• The prism manifold realization problem III
• Cable knots do not admit cosmetic surgeries
• Cosmetic surgeries on knots in S³
• Connected sums of knots do not admit purely cosmetic surgeries