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Experimental Mathematics Volume 25, 2016 - Issue 2
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Original Articles

Exact Computation of the n-Loop Invariants of Knots

Stavros GaroufalidisSchool of Mathematics, Georgia Institute of Technology, Atlanta, GA, USACorrespondence[email protected]
,
Eric SaboSchool of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA
&
Shane ScottSchool of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA
Pages 125-129 | Published online: 02 Dec 2015

References

  • [Bosma et al. 97] Wieb Bosma, John Cannon, and Catherine Playoust. “The Magma Algebra System. I. The User Language.” J. Symbol. Comput. 24:3–4 (1997), 235–265. Computational algebra and number theory (London, 1993).
  • [Culler et al. 09] Marc Culler, Nathan M. Dunfield, and Jeffery R. Weeks. “SnapPy.” Available at http://www.math.uic.edu/t3m/SnapPy, 2009.
  • [Dimofte and Garoufalidis 13] Tudor Dimofte and Stavros Garoufalidis. “The Quantum Content of the Gluing Equations.” Geom. Topol. 17:3 (2013), 1253–1315.
  • [Garoufalidis 08] Stavros Garoufalidis. “Chern-Simons Theory, Analytic Continuation and Arithmetic.” Acta Math. Vietnam. 33:3 (2008), 335–362.
  • [Garoufalidis et al. 15a] Stavros Garoufalidis, Matthias Goerner, and Christian Zickert. “The Ptolemy Field of 3-Manifold Representations.” Algebr. Geom. Topol. 15:1 (2015), 371–397.
  • [Garoufalidis et al. 15b] Stavros Garoufalidis, Eric Sabo, and Shane Scott. Available at http://www.math.gatech.edu/~stavros/publications/nloop.data/index.html/, 2015.
  • [Gukov 05] Sergei Gukov. “Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial.” Commun. Math. Phys. 255:3 (2005), 577–627.
  • [Garoufalidis and Zagier 13] Stavros Garoufalidis and Don Zagier. “Asymptotics of Quantum Knot Invariants.” Preprint, 2013.
  • [Jones 87] V. F. R. Jones. “Hecke Algebra Representations of Braid Groups and Link Polynomials.” Ann. Math. (2) 126:2 (1987), 335–388.
  • [Kashaev 95] Rinat M. Kashaev. “A Link Invariant from Quantum Dilogarithm.” Mod. Phys. Lett. A 10:19 (1995), 1409–1418.
  • [Kashaev 97] R. M. Kashaev. “The Hyperbolic Volume of Knots from the Quantum Dilogarithm.” Lett. Math. Phys. 39:3 (1997), 269–275.
  • [Murakami and Murakami 01] Hitoshi Murakami and Jun Murakami. “The Colored Jones Polynomials and the Simplicial Volume of a Knot.” Acta Math. 186:1 (2001), 85–104.
  • [Neumann and Reid 92] Walter D. Neumann and Alan W. Reid. “Arithmetic of Hyperbolic Manifolds.” In Topology ’90, Columbus, OH, 1990, Ohio State Univ. Math. Res. Inst. Publ., vol. 1, pp. 273–310. Berlin: de Gruyter, 1992.
  • [Neumann and Zagier 85] Walter D. Neumann and Don Zagier. “Volumes of Hyperbolic Three-Manifolds.” Topology 24:3 (1985), 307–332.
  • [Suslin 90] Andrei Suslin. “K3 of a Field, and the Bloch Group.” Trudy Mat. Inst. Steklov. 183 (1990), 180–199, 229. Translated in Proc. Steklov Inst. Math. 1991, no. 4, 217–239, Galois theory, rings, algebraic groups and their applications (Russian).
  • [Thurston 77] William Thurston. The Geometry and Topology of 3-Manifolds. Berlin: Universitext, Springer-Verlag, 1977. Lecture notes, Princeton.
  • [Zickert 09] Christian K. Zickert. “The Extended Bloch Group and Algebraic K-Theory.” Preprint, arXiv:0910.4005, 2009.

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