Bibliography

[Ada94] Colin C. Adams. The knot book. W. H. Freeman & Co.. 1994.

[Ago11] Ian Agol. Ideal triangulations of pseudo-Anosov mapping tori. Topology and Geometry in Dimension Three. vol. 560 of Contemp. Math.. pp. 1–17. Amer. Math. Soc.. Providence, RI. 2011.

[Bud08] Ryan Budney. Embeddings of 3-manifolds in S⁴ from the point of view of the 11-tetrahedron census. Preprint. arXiv:0810.2346. October 2008.

[Bur03] Benjamin A. Burton. Minimal triangulations and normal surfaces. PhD Thesis. University of Melbourne. May 2003. Available from the Regina website.

[Bur04] Benjamin A. Burton. Face pairing graphs and 3-manifold enumeration. J. Knot Theory Ramifications. vol. 13. no. 8. pp. 1057–1101. 2004.

[Bur07a] Benjamin A. Burton. Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find. Discrete Comput. Geom.. vol. 38. no. 3. pp. 527–571. 2007.

[Bur07b] Benjamin A. Burton. Observations from the 8-tetrahedron nonorientable census. Experiment. Math.. vol. 16. no. 2. pp. 129–144. 2007.

[Bur07c] Benjamin A. Burton. Structures of small closed non-orientable 3-manifold triangulations. J. Knot Theory Ramifications. vol. 16. no. 5. pp. 545–574. 2007.

[Bur08a] Benjamin A. Burton. Building minimal triangulations of graph manifolds using saturated blocks. In preparation. 2008.

[Bur09a] Benjamin A. Burton. Converting between quadrilateral and standard solution sets in normal surface theory. Algebr. Geom. Topol.. vol. 9. no. 4. pp. 2121–2174. 2009.

[Bur10a] Benjamin A. Burton. Optimizing the double description method for normal surface enumeration. Math. Comp.. vol. 79. no. 269. pp. 453–484. 2010.

[Bur10b] Benjamin A. Burton. Quadrilateral-octagon coordinates for almost normal surfaces. Experiment. Math.. vol. 19. no. 3. pp. 285–315. 2010.

[Bur11a] Benjamin A. Burton. Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations. ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation. pp. 59–66. ACM. 2011.

[Bur11b] Benjamin A. Burton. The Pachner graph and the simplification of 3-sphere triangulations. SCG '11: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry. pp. 153–162. ACM. 2011.

[Bur11c] Benjamin A. Burton. Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations. Preprint. arXiv:1110.6080. October 2011.

[Bur13] Benjamin A. Burton. Computational topology with Regina: Algorithms, heuristics and implementations. Geometry and Topology Down Under. vol. 597 of Contemp. Math.. pp. 195–224. Amer. Math. Soc.. Providence, RI. 2013.

[Bur14a] Benjamin A. Burton. Enumerating fundamental normal surfaces: Algorithms, experiments and invariants. ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments. pp. 112–124. SIAM. 2014.

[Bur14b] Benjamin A. Burton. A new approach to crushing 3-manifold triangulations. Discrete Comput. Geom.. vol. 52. no. 1. pp. 116–139. 2014.

[Bur14c] Benjamin A. Burton. The cusped hyperbolic census is complete. Preprint. arXiv:1405.2695. May 2014.

[Bur18] Benjamin A. Burton. The HOMFLY-PT polynomial is fixed-parameter tractable. 34th International Symposium on Computational Geometry (SoCG 2018). vol. 99 of Leibniz Int. Proc. Inform.. pp. 18:1–18:14. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik. Dagstuhl, Germany. 2018.

[Bur20] Benjamin A. Burton. The next 350 million knots. 36th International Symposium on Computational Geometry (SoCG 2020). vol. 164 of Leibniz Int. Proc. Inform.. pp. 25:1–25:17. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik. Dagstuhl, Germany. 2020.

[BCT13] Benjamin A. Burton, Alexander Coward, and Stephan Tillmann. Computing closed essential surfaces in knot complements. SCG '13: Proceedings of the 29th Annual Symposium on Computational Geometry. pp. 405–414. ACM. 2013.

[BMS15] Benjamin A. Burton, Clément Maria, and Jonathan Spreer. Algorithms and complexity for Turaev-Viro invariants. ICALP 2015: Automata, Languages, and Programming: 42nd International Colloquium. vol. 9134 of Lecture Notes in Comput. Sci.. pp. 281–293. Springer. 2015.

[BO12] Benjamin A. Burton and Melih Ozlen. A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour. Preprint. arXiv:1211.1079. November 2012.

[BO13] Benjamin A. Burton and Melih Ozlen. A tree traversal algorithm for decision problems in knot theory and 3-manifold topology. Algorithmica. vol. 65. no. 4. pp. 772–801. 2013.

[BRT12] Benjamin A. Burton, J. Hyam Rubinstein, and Stephan Tillmann. The Weber-Seifert dodecahedral space is non-Haken. Trans. Amer. Math. Soc.. 364. 2. pp. 911–932. 2012.

[CHW99] Patrick J. Callahan, Martin V. Hildebrand, and Jeffrey R. Weeks. A census of cusped hyperbolic 3-manifolds. Math. Comp.. vol. 68. no. 225. pp. 321–332. 1999.

[CT09] Daryl Cooper and Stephan Tillmann. The Thurston norm via normal surfaces. Pacific J. Math.. vol. 239. pp. 1–15. 2009.

[FG11] David Futer and François Guéritaud. From angled triangulations to hyperbolic structures. Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory. vol. 541 of Contemp. Math.. pp. 159–182. Amer. Math. Soc.. Providence, RI. 2011.

[GAP02] The GAP Group. GAP — Groups, Algorithms and Programming. Version 4.3. 2002. Available from http://www.gap-system.org/.

[Hak62] Wolfgang Haken. Über das Homöomorphieproblem der 3-Mannigfaltigkeiten. I. Math. Z.. vol. 80. pp. 89–120. 1962.

[Har20] Robert Cyrus Haraway, III. Determining hyperbolicity of compact orientable 3-manifolds with torus boundary. J. Comput. Geom.. vol. 11. no. 1. pp. 125–136. 2020.

[HLP99] Joel Hass, Jeffrey C. Lagarias, and Nicholas Pippenger. The computational complexity of knot and link problems. J. Assoc. Comput. Mach.. vol. 46. no. 2. pp. 185–211. 1999.

[HRST11] Craig D. Hodgson, J. Hyam Rubinstein, Henry Segerman, and Stephan Tillmann. Veering triangulations admit strict angle structures. Geom. Topol.. vol. 15. no. 4. pp. 2073–2089. 2011.

[HW94] Craig D. Hodgson and Jeffrey R. Weeks. Symmetries, isometries and length spectra of closed hyperbolic three-manifolds. Experiment. Math.. vol. 3. no. 4. pp. 261–274. 1994.

[JO84] William Jaco and Ulrich Oertel. An algorithm to decide if a 3-manifold is a Haken manifold. Topology. vol. 23. no. 2. pp. 195–209. 1984.

[JR03] William Jaco and J. Hyam Rubinstein. 0-efficient triangulations of 3-manifolds. J. Differential Geom.. vol. 65. no. 1. pp. 61–168. 2003.

[JR06] William Jaco and J. Hyam Rubinstein. Layered-triangulations of 3-manifolds. Preprint. February 2006.

[KR05] Ensil Kang and J. Hyam Rubinstein. Ideal triangulations of 3-manifolds II; Taut and angle structures. Algebr. Geom. Topol.. vol. 5. pp. 1505–1533. 2005.

[KK80] Akio Kawauchi and Sadayoshi Kojima. Algebraic classification of linking pairings on 3-manifolds. Math. Ann.. vol. 253. no. 1. pp. 29–42. 1980.

[Lac00a] Marc Lackenby. Taut ideal triangulations of 3-manifolds. Geom. Topol.. vol. 4. pp. 369–395 (electronic). 2000.

[Lac00b] Marc Lackenby. Word hyperbolic Dehn surgery. Invent. Math.. vol. 140. no. 2. pp. 243–282. 2000.

[MP01] Bruno Martelli and Carlo Petronio. Three-manifolds having complexity at most 9. Experiment. Math.. vol. 10. no. 2. pp. 207–236. 2001.

[Mat98] Sergei V. Matveev. Tables of 3-manifolds up to complexity 6. Max-Planck-Institut für Mathematik Preprint Series. vol. 67. 1998. Available from http://www.mpim-bonn.mpg.de/html/preprints/preprints.html.

[Riv94] Igor Rivin. Euclidean structures on simplicial surfaces and hyperbolic volume. Ann. of Math. (2). vol. 139. no. 3. pp. 553–580. 1994.

[Riv03] Igor Rivin. Combinatorial optimization in geometry. Adv. in Appl. Math.. vol. 31. no. 1. pp. 242–271. 2003.

[Rub95] J. Hyam Rubinstein. An algorithm to recognize the 3-sphere. Proceedings of the International Congress of Mathematicians (Zürich, 1994). vol. 1. pp. 601–611. Birkhäuser. Basel. 1995.

[Rub97] J. Hyam Rubinstein. Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3-dimensional manifolds. Geometric Topology (Athens, GA, 1993). vol. 2 of AMS/IP Stud. Adv. Math.. pp. 1–20. Amer. Math. Soc.. Providence, RI. 1997.

[Tho94] Abigail Thompson. Thin position and the recognition problem for S³. Math. Res. Lett.. vol. 1. no. 5. pp. 613–630. 1994.

[Til08] Stephan Tillmann. Normal surfaces in topologically finite 3-manifolds. Enseign. Math. (2). vol. 54. pp. 329–380. 2008.

[Tol98] Jeffrey L. Tollefson. Normal surface Q-theory. Pacific J. Math.. vol. 183. no. 2. pp. 359–374. 1998.

[TV92] Vladimir G. Turaev and Oleg Y. Viro. State sum invariants of 3-manifolds and quantum 6j-symbols. Topology. vol. 31. no. 4. pp. 865–902. 1992.

[Wee93] Jeffrey R. Weeks. Convex hulls and isometries of cusped hyperbolic 3-manifolds. Topology Appl.. vol. 52. pp. 127–149. 1993.