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The prism manifold realization problem

Ballinger, William and Hsu, Chloe Ching-Yun and Mackey, Wyatt and Ni, Yi and Ochse, Tynan and Vafaee, Faramarz (2016) The prism manifold realization problem. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180308-070142351

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Abstract

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 the classification is similar to that of Greene for lens spaces.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1612.04921arXivDiscussion Paper
Additional Information:Y.N. was partially supported by NSF grant number DMS-1252992 and an Alfred P. Sloan Research Fellowship. W.B., C.H., W.M. and T.O. were supported by Caltech’s Summer Undergraduate Research Fellowships (SURF) program. W.B. also wishes to thank Samuel P. and Frances Krown for their generous support through the SURF program. We are grateful to John Berge for sending us the preprint [2] and some useful programs.
Funders:
Funding AgencyGrant Number
NSFDMS-1252992
Alfred P. Sloan FoundationUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Record Number:CaltechAUTHORS:20180308-070142351
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180308-070142351
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85187
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Mar 2018 16:56
Last Modified:08 Mar 2018 16:56

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