| dc.contributor.author | Haraway, Robert, III | |
| dc.contributor.author | Hoffman, Neil R. | |
| dc.date.accessioned | 2022-11-07T14:33:48Z | |
| dc.date.available | 2022-11-07T14:33:48Z | |
| dc.date.issued | 2019-07-02 | |
| dc.identifier.citation | Haraway, R.H., III, Hoffman, N.R. (2019). On the complexity of cusped non-hyperbolicity. | |
| dc.identifier.uri | https://hdl.handle.net/11244/336603 | |
| dc.description.abstract | We show that the problem of showing that a cusped 3-manifold M is not hyperbolic is in NP, assuming S3-RECOGNITION is in coNP. To this end, we show that IRREDUCIBLE TOROIDAL RECOGNITION lies in NP. Along the way we unconditionally recover SATELLITE KNOT RECOGNITION lying in NP. This was previously known only assuming the Generalized Riemann Hypothesis. Our key contribution is to certify closed essential normal surfaces as essential in polynomial time in compact orientable irreducible ∂-irreducible triangulations. Our work is made possible by recent work of Lackenby showing several basic decision problems in 3-manifold topology are in NP or coNP. | |
| dc.format | application/pdf | |
| dc.relation.uri | http://arxiv.org/abs/1907.01675v3 | |
| dc.rights | This material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information. | |
| dc.title | On the complexity of cusped non-hyperbolicity | |
| dc.date.updated | 2022-10-26T21:02:53Z | |
| dc.description.department | Mathematics | |
| dc.type.genre | Preprint | |
| dc.type.material | Text | |
| dc.subject.keywords | math.GT: Geometric Topology | |
| dc.subject.keywords | 68Q25: Analysis of algorithms and problem complexity | |
| dc.subject.keywords | 57M50: General geometric structures on low-dimensional manifolds | |
| dc.identifier.author | ORCID: 0000-0003-0662-3244 (Hoffman, Neil R) | |
| dc.identifier.author | ScopusID: 16642919400 (Hoffman, Neil R) | |
