236
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Verified Computations for Hyperbolic 3-Manifolds

, , , , &

REFERENCES

  • [Benedetti and Petronio 92] R. Benedetti and C. Petronio. Lectures on Hyperbolic Geometry, Universitext. Berlin: Springer-Verlag, 1992.
  • [Burton, to appear] B. Burton. “The Cusped Hyperbolic Census is Complete.” To appear in Transactions of the American Mathematics Society.
  • [Callahan et al. 99] P. Callahan, M. Hildebrand, and J. Weeks. “A Census of Cusped Hyperbolic 3-Manifolds.” Math. Comp. 68: 225 (1999), 321–332.
  • [Coulson et al. 00] D. Coulson, O. Goodman, C. Hodgson, and W. Neumann. “Computing Arithmetic Invariants of 3-Manifolds.” Exp. Math. 9: 1 (2000), 127–152.
  • [Culler et al.] M. Culler, N. M. Dunfield, and J. R. Weeks. “SnapPy, A Computer Program for Studying the Geometry and Topology of 3-Manifolds.” Available at http://snappy.computop.org.
  • [Gabai et al. 03] D. Gabai, R. Meyerhoff, and N. Thurston. “Homotopy Hyperbolic 3-Manifolds are Hyperbolic.” Ann. Math. 157: 2 (2003), 335–431.
  • [Goodman] O. Goodman. “Snap, based on the SnapPea Kernel of Jeff Weeks and the Pari Software.” Available at http://sourceforge.net/projects/snap-pari.
  • [Hodgson and Weeks 94] C. Hodgson and J. Weeks. “Symmetries, Isometries and Length Spectra of Closed Hyperbolic Three-Manifolds.” Exp. Math. 3 (1994), 261–274.
  • [Hoffman et al.] N. Hoffman, K. Ichihara, M. Kashiwagi, H. Masai, S. Oishi, and A. Takayasu. “hikmot”. Available at http://www.oishi.info.waseda.ac.jp/~takayasu/hikmot/.
  • [Ichihara and Masai, to appear] K. Ichihara, and H. Masai. “Exceptional Surgeries on Alternating Knots.” To appear in Communications in Analysis and Geometry.
  • [IEEE 754 08] IEEE 754. ANSI/IEEE 754-2008: IEEE Standard for Floating-Point Arithmetic. New York: IEEE, 2008.
  • [Kantorovich and Akilov 64] L. V. Kantorovich and G. P. Akilov. Functional Analysis in Normed Spaces. Oxford: Pergamon Press, 1964.
  • [Krawczyk 69] R. Krawczyk. “Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken.” Computing 4 (1969), 187–201.
  • [Krawczyk 69] R. Krawczyk. “Fehlerabschätzung reeller Eigenwerte und Eigenvektoren von Matrizen.” Computing 4 (1969), 281–293.
  • [Markov and Okumura 99] S. Markov and K. Okumura. “The Contribution of T. Sunaga to Interval Analysis and Reliable Computing.” T. Csendes (Ed.) In Developments in Reliable Computing, pp. 167–188. Dordrecht, Netherlands: Kluwer, 1999.
  • [Martelli et al. 14] B. Martelli, C. Petronio, and F. Roukema. “Exceptional Dehn Surgery on the Minimally Twisted Five-Chain Link.” Commun. Anal. Geom. 22: 4 (2014), 689–735.
  • [Matsuoka et al. 10] S. Matsuoka, T. Endo, N. Maruyama, H. Sato, and S. Takizawa. “The Total Picture of TSUBAME2.0.” TSUBAME E-Sci. J. 1 (2010), 16–18. Tokyo Tech. GSIC.
  • [Moore 66] R. E. Moore. Interval Analysis. Englewood Cliffs: Prentice-Hall, 1966.
  • [Moser 09] H. Moser. “Proving a Manifold to be Hyperbolic Once it has been Approximated to be so.” Algebraic Geom. Topol. 9 (2009), 103–133. Code associated to the paper is available here: http://www.math.columbia.edu/ moser/.
  • [Neumann and Zagier 85] W. Neumann and D. Zagier. “Volumes of Hyperbolic Three-Manifolds.” Topology 24: 3 (1985), 307–332.
  • [Rall 81] L. B. Rall. Automatic Differentiation: Techniques and Applications. Lecture Notes in Computer Science, vol. 120. Springer, 1981.
  • [Neidinger 10] R. D. Neidinger. “Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming.” SIAM Rev. 52: 3 (2010), 545–563.
  • [Rump 10] S. M. Rump. “Verification Methods: Rigorous Results using Floating-Point Arithmetic.” Acta Numer. 19 (2010), 287–449.
  • [Sunaga 56] T. Sunaga. “Geometry of Numerals.” Master’s thesis, University of Tokyo, 1956.
  • [Sunaga 58] T. Sunaga. “Theory of an Interval Algebra and its Application to Numerical Analysis.” RAAG Memoirs 2 (1958), 29–46.
  • [Thurston 78] W. P. Thurston. The Geometry and Topology of 3-Manifolds. Lecture Notes. Princeton University, 1978.
  • [Thurston 82] W. P. Thurston. “Three-Dimensional Manifolds, Kleinian Groups and Hyperbolic Geometry.” Bull. Am. Math. Soc. (N.S.) 6: 3 (1982), 357–381.
  • [Tokyo Institute of Technology] Tokyo Institute of Technology. The Global Scientific Information and Computing Center. TSUBAME. Available at http://tsubame.gsic.titech.ac.jp/en.
  • [Weeks 05] J. Weeks. “Computation of Hyperbolic Structures in Knot Theory.” In Handbook of Knot Theory, pp. 461–480. Elsevier Science, 2005.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.