[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.

[Bur14] Benjamin A. Burton. Enumerating fundamental normal surfaces: Algorithms, experiments and invariants. ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments. arXiv:1111.7055. To appear.

[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.

[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.

[GAP02] The GAP Group. GAP — Groups, Algorithms and Programming. Version 4.3. 2002. Available from

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

[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

[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.