Quadrilateral–Octagon Coordinates for Almost Normal Surfaces

REFERENCES

• Agol , Ian , Hass , Joel and Thurston , William . “3-Manifold Knot Genus is NP-Complete.” . STOC 1902: Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing . pp. 761 – 766 . New York : ACM Press. . [Agol et al. 02]
   Google Scholar
• Burton , Benjamin A. 2003 . “Minimal Triangulations and Normal Surfaces.” , PhD thesis University of Melbourne. . Available online http://regina.sourceforge.net/[Burton 03]
   Google Scholar
• Burton , Benjamin A. 2004 . “Introducing Regina, the 3-Manifold Topology Software.” . Experiment. Math. , 13 ( 3 ) : 267 – 272 . [Burton 04]
   Web of Science ®Google Scholar
• Burton , Benjamin A. 1999–2009 . “Regina: Normal Surface and 3-Manifold Topology Software.” Available online http://regina.sourceforge.net/[Burton 09a]
   Google Scholar
• Burton , Benjamin A. 2009 . “Converting between Quadrilateral and Standard Solution Sets in Normal Surface Theory.” . Algebr. Geom. Topol. , 9 ( 4 ) : 2121 – 2174 . [Burton 09b]
   Google Scholar
• Burton , Benjamin A. 2010 . “Optimizing the Double Description Method for Normal Surface Enumeration.” . Math. Comp. , 79 : 453 – 484 . [Burton 10a]
   Google Scholar
• Burton , Benjamin A. “The Complexity of the Normal Surface Solution Space.” . SCG '10: Proccedings of the Twenty-Sixth Annual Symposium on Computational Geometry . pp. 201 – 209 . New York : ACM. . [Burton 10b]
   Google Scholar
• Haken , Wolfgang . 1961 . “Theorie der Normalflächen.” . Acta Math , 105 : 245 – 375 . [Haken 61]
   Web of Science ®Google Scholar
• Haken , Wolfgang . 1962 . “Über das Homöomorphieproblem der 3-Mannigfaltigkeiten I.” . Math. Z. , 80 : 89 – 120 . [Haken 62]
   Google Scholar
• Hass , Joel , Lagarias , Jeffrey C. and Pippenger , Nicholas . 1999 . “The Computational Complexity of Knot and Link Problems.” . J. Assoc. Comput. Mach. , 46 ( 2 ) : 185 – 211 . [Hass et al. 99]
   Web of Science ®Google Scholar
• Hildebrand , Martin V. and Weeks , Jeffrey R. 1989 . “A Computer Generated Census of Cusped Hyperbolic 3-Manifolds.” . In Computers and Mathematics (Cambridge, MA, 1989) 53 – 59 . New York : Springer. . [Hildebrand and Weeks 89]
   Google Scholar
• Hodgson , Craig D. and Weeks , Jeffrey R. 1994 . “Symmetries, Isometries and Length Spectra of Closed Hyperbolic Three-Manifolds.” . Experiment. Math. , 3 ( 4 ) : 261 – 274 . [Hodgson and Weeks 94]
   Google Scholar
• Jaco , William and Oertel , Ulrich . 1984 . “An Algorithm to Decide If a 3-Manifold Is a Haken Manifold.” . Topology , 23 ( 2 ) : 195 – 209 . [Jaco and Oertel 84]
   Web of Science ®Google Scholar
• Jaco , William and Hyam Rubinstein , J. 2003 . “0-Efficient Triangulations of 3-Manifolds.” . J. Differential Geom. , 65 ( 1 ) : 61 – 168 . [Jaco and Rubinstein 03]
   Google Scholar
• Jaco , William and Tollefson , Jeffrey L. 1995 . “Algorithms for the Complete Decomposition of a Closed 3-Manifold.” . Illinois J. Math. , 39 ( 3 ) : 358 – 406 . [Jaco and Tollefson 95]
   Web of Science ®Google Scholar
• Jaco , William , Letscher , David and Hyam Rubinstein , J. 2002 . “Algorithms for Essential Surfaces in 3-Manifolds.” . In Topology and Geometry: Commemorating SISTAGx, Contemporary Mathematics 314“Algorithms for Essential Surfaces in 3-Manifolds.” 107 – 124 . Providence : Amer. Math. Soc. . [Jaco et al. 02]
   Google Scholar
• Kneser , Hellmuth . 1929 . “Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten.” . Jahresbericht der Deutschen Math. Verein. , 38 : 248 – 260 . [Kneser 29]
   Google Scholar
• Lackenby , Marc . 2008 . “An Algorithm to Determine the Heegaard Genus of Simple 3-Manifolds with Nonempty Boundary.” . Algebr. Geom. Topol. , 8 ( 2 ) : 911 – 934 . [Lackenby 08]
   Google Scholar
• Motzkin , T. S. , Raiffa , H. , Thompson , G. L. and Thrall , R. M. 1953 . “The Double Description Method.” . In Contributions to the Theory of Games Edited by: Kuhn , H. W. and Tucker , A. W. Vol. II , 51 – 73 . Princeton : Princeton University Press. . Annals of Mathematics Studies 28, [Motzkin et al. 53]
   Google Scholar
• Hyam Rubinstein , J. “An Algorithm to Recognize the 3-Sphere.” . Proceedings of the International Congress of Mathematicians (Zürich, 1994) . Vol. 1 , pp. 601 – 611 . Basel : Birkhäuser. . [Rubinstein 95]
   Google Scholar
• Hyam Rubinstein , J. 1997 . “Polyhedral Minimal Surfaces, Heegaard Splittings and Decision Problems for 3-Dimensional Manifolds.” . In Geometric Topology (Athens, GA, 1993) Vol. 2 , 1 – 20 . Providence : Amer. Math. Soc. . AMS/IP Stud. Adv. Math., [Rubinstein 97]
   Google Scholar
• Hyam Rubinstein , J. 2004 . “An Algorithm to Recognise Small Seifert Fiber Spaces.” . Turkish J. Math. , 28 ( 1 ) : 75 – 87 . [Rubinstein 04]
   Google Scholar
• Thompson , Abigail . 1994 . “Thin Position and the Recognition Problem for S3.” . Math. Res. Lett. , 1 ( 5 ) : 613 – 630 . [Thompson 94]
   Google Scholar
• Thurston , William P. 1978 . “The Geometry and Topology of 3-Manifolds.” Lecture notes, Princeton University. . [Thurston 78]
   Google Scholar
• Tillmann , Stephan . 2008 . “Normal Surfaces in Topologically Finite 3-Manifolds.” . Enseign. Math. (2) , 54 : 329 – 380 . [Tillmann 08]
   Google Scholar
• Tollefson , Jeffrey L. 1998 . “Normal Surface Q-Theory.” . Pacific J. Math. , 183 ( 2 ) : 359 – 374 . [Tollefson 98]
   Web of Science ®Google Scholar
• Wilson , Robin Todd . 2008 . “Meridional Almost Normal Surfaces in Knot Complements.” . Algebr. Geom. Topol. , 8 ( 3 ) : 1717 – 1740 . [Wilson 08]
   Google Scholar