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2020 The prism manifold realization problem
William Ballinger, Chloe Ching-Yun Hsu, Wyatt Mackey, Yi Ni, Tynan Ochse, Faramarz Vafaee
Algebr. Geom. Topol. 20(2): 757-816 (2020). DOI: 10.2140/agt.2020.20.757

Abstract

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.

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William Ballinger. Chloe Ching-Yun Hsu. Wyatt Mackey. Yi Ni. Tynan Ochse. Faramarz Vafaee. "The prism manifold realization problem." Algebr. Geom. Topol. 20 (2) 757 - 816, 2020. https://doi.org/10.2140/agt.2020.20.757

Information

Received: 17 May 2018; Revised: 6 June 2019; Accepted: 24 June 2019; Published: 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07195376
MathSciNet: MR4092311
Digital Object Identifier: 10.2140/agt.2020.20.757

Subjects:
Primary: 57M25, 57R65

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 2 • 2020
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