The prism manifold realization problem

Ballinger, William¹ ; Hsu, Chloe² ; Mackey, Wyatt³ ; Ni, Yi² ; Ochse, Tynan⁴ ; Vafaee, Faramarz⁵

¹Department of Mathematics, Princeton University, Princeton, NJ, United States
²Department of Mathematics, California Institute of Technology, Pasadena, CA, United States
³Department of Mathematics, Stanford University, Stanford, CA, United States
⁴Department of Mathematics, University of Texas, Austin, Austin, TX, United States
⁵Department of Mathematics, Duke University, Durham, NC, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 757-816

Résumé

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S3 . 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 list of prism manifolds P(p,q) that can possibly be realized by positive integral surgeries on knots in S3 when q < 0. Based on the forthcoming work of Berge and Kang, we are confident that this list is complete. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces.

Détail

DOI : 10.2140/agt.2020.20.757

Classification : 57M25, 57R65
Keywords: prism manifold, Dehn surgery, changemaker

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