Non-geometric Veering Triangulations

References

• [Agol 11] Ian Agol. “Ideal Triangulations of Pseudo-Anosov Mapping Tori.” In Topology and Geometry in Dimension Three, Contemp. Math. 560, pp. 1–17. Amer. Math. Soc., 2011.
   Google Scholar
• [Bell, Hall, and Schleimer 12] Mark Bell, Tracy Hall, and Saul Schleimer. Twister [computer software]. http://surfacebundles.wordpress.com/, 2012. Included with SnapPy version 1.5.
   Google Scholar
• [Bestvina and Handel 95] M. Bestvina and M. Handel. “Train-Tracks for Surface Homeomorphisms.” Topology 34 (1995), 109–140.
   Web of Science ®Google Scholar
• [Burton 99/13] Benjamin A. Burton. Regina: Normal surface and 3-manifold topology software. http://regina.sourceforge.net, 1999–2013.
   Google Scholar
• [Calegari 07] Danny Calegari. Foliations and the Geometry of 3-Manifolds, Oxford Mathematical Monographs. Oxford University Press, 2007.
   Google Scholar
• [Casson and Bleiler 83] A. Casson and S. Bleiler. “Automorphisms of Surfaces after Nielsen and Thurston.” Handwritten notes, University of Texas at Austin. Volume 1, fall 1982; volume 2, spring 1983.
   Google Scholar
• [Casson and Bleiler 88] Andrew J. Casson and Steven A. Bleiler. Automorphisms of Surfaces after Nielsen and Thurston, London Mathematical Society Student Texts 9. Cambridge University Press, 1988.
   Google Scholar
• [Coulson et al. 00] David Coulson, Oliver A. Goodman, Craig D. Hodgson, and Walter D. Neumann. “Computing Arithmetic Invariants of 3-Manifolds.” Experiment. Math. 9 (2000), 127–152.
   Web of Science ®Google Scholar
• [Culler and Dunfield 12] Marc Culler and Nathan Dunfield. SnapPy (version 1.5) [computer software]. http://www.math.uic.edu/t3m/SnapPy/, 2012. Uses the SnapPea kernel written by Jeff Weeks.
   Google Scholar
• [Farb and Margalit 12] Benson Farb and Dan Margalit. A Primer on Mapping Class Groups, Princeton Mathematical Series 49. Princeton University Press, 2012.
   Google Scholar
• [Fathi et al. 12] A. Fathi, F. Laudenbach, V. Poénaru, et al. Thurston’s Work on Surfaces, translated from the French original by Djun Kim and Dan Margalit. Princeton University Press, 2012.
   Google Scholar
• [Francaviglia 04] Stefano Francaviglia. “Hyperbolicity Equations for Cusped 3-Manifolds and Volume-Rigidity of Representations.” PhD thesis, Scuola Normale Superiore, Pisa, Italy, 2004.
   Google Scholar
• [Futer and Guéritaud 13] David Futer and François Guéritaud. “Explicit Angle Structures for Veering Triangulations.” Algebr. Geom. Topol. 13 (2013), 205–235.
   Web of Science ®Google Scholar
• [Goodman 10] Oliver Goodman. Snap (version 1.11.3) [computer software]. http://sourceforge.net/projects/snap-pari/, 2010. Uses the SnapPea kernel written by Jeff Weeks.
   Google Scholar
• [Guéritaud 06] François Guéritaud. “On Canonical Triangulations of Once-Punctured Torus Bundles and Two-Bridge Link Complements.” Geom. Topol. 10 (2006), 1239–1284.
   Web of Science ®Google Scholar
• [Hall 09] Toby Hall. Trains (version 4.32, 2009) [computer software]. http://www.liv.ac.uk/∼tobyhall/THall.html. An implementation of the Bestvina-Handel algorithm.
   Google Scholar
• [Hemion 79] Geoffrey Hemion. “On the Classification of Homeomorphisms of 2-Manifolds and the Classification of 3-Manifolds.” Acta Math. 142 (1979), 123–155.
   Google Scholar
• [Hodgson et al. 11] Craig D. Hodgson, J. Hyam Rubinstein, Henry Segerman, and Stephan Tillmann. “Veering Triangulations Admit Strict Angle Structures.” Geom. Topol. 15 (2011), 2073–2089.
   Web of Science ®Google Scholar
• [Issa 12] Ahmad Issa. “Construction of Non-geometric Veering Triangulations of Fibered Hyperbolic 3-Manifolds.” MSc thesis, University of Melbourne, Melbourne, Australia, 2012.
   Google Scholar
• [Issa 13] Ahmad Issa. Veering (July 2013) [computer software]. http://www.ms.unimelb.edu.au/∼veering/. Uses the Trains program written by Toby Hall.
   Google Scholar
• [Kozai 13] Kenji Kozai. “Singular Hyperbolic Structures on Pseudo-Anosov Mapping Tori.” PhD thesis, Stanford University, Palo Alto, California, 2013.
   Google Scholar
• [Kozai 14] Kenji Kozai. “Hyperbolic Structures from Sol on Pseudo-Anosov Mapping Tori.” arXiv:1406.5900 [math.GT], 2014.
   Google Scholar
• [Lackenby 03] Marc Lackenby. “The Canonical Decomposition of Once-Punctured Torus Bundles.” Comment. Math. Helv. 78 (2003), 363–384.
   Web of Science ®Google Scholar
• [Menasco and Thistlethwaite 05] William Menasco and Morwen Thistlethwaite, editors. Handbook of Knot Theory. Elsevier, 2005.
   Google Scholar
• [Mosher 83] Lee Mosher. “Pseudo-Anosovs on Punctured Surfaces.” PhD thesis, Princeton University, 1983.
   Google Scholar
• [Mosher 86] Lee Mosher. “The Classification of Pseudo-Anosovs.” In Low-Dimensional Topology and Kleinian Groups (Coventry/Durham, 1984), London Math. Soc. Lecture Note Ser. 112, pp. 13–75. Cambridge Univ. Press, 1986.
   Google Scholar
• [Mosher 03] Lee Mosher. “Train Track Expansions of Measured Foliations.” Preprint, December 2003.
   Google Scholar
• [Neumann and Yang 99] Walter D. Neumann and Jun Yang. “Bloch Invariants of Hyperbolic 3-Manifolds.” Duke Math. J. 96 (1999), 29–59.
   Web of Science ®Google Scholar
• [Penner and Harer 92] R. C. Penner and J. L. Harer. Combinatorics of Train Tracks, Annals of Mathematics Studies 125. Princeton University Press, 1992.
   Google Scholar
• [Segerman 12] Henry Segerman. “A Generalisation of the Deformation Variety.” Algebr. Geom. Topol. 12 (2012), 2179–2244.
   Web of Science ®Google Scholar
• [Thurston 79] W. P. Thurston. “The Geometry and Topology of 3-Manifolds.” Mimeographed notes, Princeton University Mathematics Department, 1979.
   Google Scholar
• [Weeks 85/07] Jeffrey Weeks. SnapPea [computer software]. http://www.geometrygames.org/SnapPea/, 1985–2007.
   Google Scholar