Volume 9, issue 4 (2009)

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Converting between quadrilateral and standard solution sets in normal surface theory

Benjamin A Burton

Algebraic & Geometric Topology 9 (2009) 2121–2174
Bibliography
1 D Avis, D Bremner, R Seidel, How good are convex hull algorithms?, Comput. Geom. 7 (1997) 265 MR1447243
2 A Brøndsted, An introduction to convex polytopes, 90, Springer (1983) MR683612
3 B A Burton, Regina : Normal surface and 3–manifold topology software (1999–2009)
4 B A Burton, Introducing Regina, the 3–manifold topology software, Experiment. Math. 13 (2004) 267 MR2103324
5 B A Burton, Extreme cases in normal surface enumeration, in preparation (2009)
6 B A Burton, Optimizing the double description method for normal surface enumeration, Math. Comp. 79 (2010) 453
7 M Culler, N Dunfield, FXrays: Extremal ray enumeration software (2002–2003)
8 W Eberly, M Giesbrecht, P Giorgi, A Storjohann, G Villard, Solving sparse rational linear systems, from: "ISSAC 2006", ACM (2006) 63 MR2289102
9 K Fukuda, A Prodon, Double description method revisited, from: "Combinatorics and computer science (Brest, 1995)", Lecture Notes in Comput. Sci. 1120, Springer (1996) 91 MR1448924
10 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245 MR0141106
11 W Haken, Über das Homöomorphieproblem der 3–Mannigfaltigkeiten I, Math. Z. 80 (1962) 89 MR0160196
12 J Hass, J C Lagarias, N Pippenger, The computational complexity of knot and link problems, J. ACM 46 (1999) 185 MR1693203
13 C D Hodgson, J R Weeks, Symmetries, isometries and length spectra of closed hyperbolic three-manifolds, Experiment. Math. 3 (1994) 261 MR1341719
14 W Jaco, U Oertel, An algorithm to decide if a 3–manifold is a Haken manifold, Topology 23 (1984) 195 MR744850
15 W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
16 W Jaco, J L Tollefson, Algorithms for the complete decomposition of a closed 3–manifold, Illinois J. Math. 39 (1995) 358 MR1339832
17 H Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresbericht der Deut. Math. Verein. 38 (1929) 248
18 S Matsumoto, R Rannard, The regular projective solution space of the figure-eight knot complement, Experiment. Math. 9 (2000) 221 MR1780207
19 T S Motzkin, H Raiffa, G L Thompson, R M Thrall, The double description method, from: "Contributions to the theory of games, vol. 2", Annals of Mathematics Studies 28, Princeton University Press (1953) 51 MR0060202
20 J H Rubinstein, An algorithm to recognize the 3–sphere, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)", Birkhäuser (1995) 601 MR1403961
21 J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
22 A Thompson, Thin position and the recognition problem for S3, Math. Res. Lett. 1 (1994) 613 MR1295555
23 W P Thurston, The geometry and topology of 3–manifolds, lecture notes, Princeton University (1978)
24 S Tillmann, Normal surfaces in topologically finite 3–manifolds, Enseign. Math. (2) 54 (2008) 329 MR2478091
25 J L Tollefson, Normal surface Q–theory, Pacific J. Math. 183 (1998) 359 MR1625962