On the complexity of cusped non-hyperbolicity
| Autor: | Haraway III, Robert, Hoffman, Neil R |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that the problem of showing that a cusped 3-manifold M is not hyperbolic is in NP, assuming $S^3$-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 $\partial$-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. Comment: 30 pages; version 3 fills gap in certifying homeomorphism to 0-efficient triangulation, and corrects proofs of surface bundle recognition and essential annulus certification |
| Databáze: | arXiv |
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