Profinite Rigidity in the SnapPea Census

References

• [Agol 14] I. Agol. “Virtual Properties of 3-Manifolds.” In Proceedings of the International Congress of Mathematicians—Seoul 2014, vol. 1, pp. 141–170. Seoul: Kyung Moon Sa, 2014.
   Google Scholar
• [Baumslag et al. 04] G. Baumslag, S. Cleary, and G. Havas. “Experimenting with Infinite Groups. I.” Exp. Math. 13:4 (2004), 495–502.
   Web of Science ®Google Scholar
• [Boileau and Friedl 15] M. Boileau and S. Friedl. “The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm.” Available at https://arxiv.org/abs/1505.07799, 2015.
   Google Scholar
• [Bridson et al. 18] M. R. Bridson, D. B. McReynolds, A. W. Reid, and R. Spitler. “Absolute profinite rigidity and hyperbolic geometry.” Available at https://arxiv.org/abs/1811.04394, 2018.
   Google Scholar
• [Bridson and Reid 15] M. R. Bridson and A. W. Reid. “Profinite Rigidity, Fibering, and the Figure-Eight Knot.” Available at https://arxiv.org/abs/1505.07886, 2015.
   Google Scholar
• [Brown 87] K. S. Brown. “Trees, Valuations, and the Bieri–Neumann–Strebel Invariant.” Invent. Math. 90:3 (1987), 479–504.
   Web of Science ®Google Scholar
• [Bridson et al. 17] M. R. Bridson, A. W. Reid, and H. Wilton. “Profinite Rigidity and Surface Bundles over the Circle.” Bull. Lond. Math. Soc. 49:5 (2017), 831–841.
   Web of Science ®Google Scholar
• [Burton 14] B. A. Burton. “A Duplicate Pair in the SnapPea Census.” Exp. Math. 23:2 (2014), 170–173.
   Web of Science ®Google Scholar
• [Bridson and Wilton 15] M. R. Bridson and H. Wilton. “The Triviality Problem for Profinite Completions.” Invent. Math. 202:2 (2015), 839–874.
   Web of Science ®Google Scholar
• [Culler et al. 17] M. Culler, N. M. Dunfield, M. Goerner, and J. R. Weeks. “SnapPy, a Computer Program for Studying the Geometry and Topology of 3-Manifolds.” Available at http://snappy.computop.org, 2017.
   Google Scholar
• [Dunfield and Thurston 03] N. M. Dunfield and W. P. Thurston. “The Virtual Haken Conjecture: Experiments and Examples.” Geom. Topol. 7 (2003), 399–441.
   Web of Science ®Google Scholar
• [Gordon 72] C. M. A. Gordon. “Knots Whose Branched Cyclic Coverings Have Periodic Homology.” Trans. Amer. Math. Soc. 168 (1972), 357–370.
   Web of Science ®Google Scholar
• [The GAP Group 16] The GAP Group. “GAP—Groups, Algorithms, and Programming, Version 4.8.3.” Available at http://www.gap-system.org, 2016.
   Google Scholar
• [Hyafil and Rivest 76] L. Hyafil and R. L. Rivest. “Constructing Optimal Binary Decision Trees Is NP-Complete.” Inf. Process. Lett. 5:1 (1976), 15–17.
   Google Scholar
• [Hoste et al. 98] J. Hoste, M. Thistlethwaite, and J. Weeks. “The First 1,701,936 Knots.” Math. Intell. 20:4 (1998), 33–48.
   Web of Science ®Google Scholar
• [Jaikin-Zapirain 17] A. Jaikin-Zapirain. “Recognition of Being Fibred for Compact 3-Manifolds.” Available at http://verso.mat.uam.es/∼andrei.jaikin/preprints/fibering.pdf, 2017.
   Google Scholar
• [Lê 18] T. Lê. “Growth of homology torsion in finite coverings and hyperbolic volume.” Ann. Inst. Fourier (Grenoble) 68:2 (2018), 611–645.
   Google Scholar
• [Long and Reid 98] D. D. Long and A. W. Reid. “Simple Quotients of Hyperbolic 3-Manifold Groups.” Proc. Amer. Math. Soc. 126:3 (1998), 877–880.
   Web of Science ®Google Scholar
• [Nikolov and Segal 07] N. Nikolov and D. Segal. “On Finitely Generated Profinite Groups. I. Strong Completeness and Uniform Bounds.” Ann. Math. (2) 165:1 (2007), 171–238.
   Web of Science ®Google Scholar
• [Remeslennikov 67] V. N. Remeslennikov. “Conjugacy of Subgroups in Nilpotent Groups.” Algebra Logika Sem. 6:2 (1967), 61–76.
   Google Scholar
• [Ribes and Zalesskii 10] L. Ribes and P. Zalesskii. Profinite groups, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge/A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series], vol. 40, 2nd ed. Berlin: Springer-Verlag, 2010.
   Google Scholar
• [Seed 17] C. Seed. “knotkit.” Available at https://github.com/cseed/knotkit, 2017.
   Google Scholar
• [Thurston 82] W. P. Thurston. “Three-Dimensional Manifolds, Kleinian Groups and Hyperbolic Geometry.” Bull. Amer. Math. Soc. (N.S.) 6:3 (1982), 357–381.
   Web of Science ®Google Scholar
• [Ueki 18] J. Ueki. “The profinite completions of knot groups determine the Alexander polynomials.” Algebr. Geom. Topol. 18:5 (2018), 3013–3030.
   Google Scholar
• [Wilkes 17] G. Wilkes. “Profinite Rigidity for Seifert Fibre Spaces.” Geom. Dedicata 188 (2017), 141–163.
   Web of Science ®Google Scholar
• [Wilton and Zalesskii 17] H. Wilton and P. Zalesskii. “Distinguishing Geometries Using Finite Quotients.” Geom. Topol. 21:1 (2017), 345–384.
   Web of Science ®Google Scholar