Character Varieties For : The Figure Eight Knot

References

• [Bergeron et al. 11] N. Bergeron, E. Falbel, and A. Guilloux. “Tetrahedra of Flags, Volume and Homology of SL(3).” arXiv:1101.2742. To appear in Geom. Top., 2011.
   Google Scholar
• [Bergeron et al. 13] N. Bergeron, E. Falbel, A. Guilloux, P. V. Koseleff, and F. Rouillier. “Local Rigidity For Representations of 3-Manifold Groups.” Exp. Math. 22: 4 (2013), 410–420.
   Web of Science ®Google Scholar
• [Brehm 90] U. Brehm. “The Shape Invariant of Triangles and Trigonometry in Two-Point Homogeneous Spaces.” Geom. Dedicata 33: 1 (1990), 59–76.
   Web of Science ®Google Scholar
• [Champanerkar 03] A. Champanerkar. “A-Polynomial and Bloch Invariants of Hyperbolic 3-Manifolds.” PhD diss., Columbia University, 2003.
   Google Scholar
• [Cooper 06] D. Cooper, D. D. Long, and M. B. Thistlethwaite. “Computing Varieties of Representations of Hyperbolic 3-Manifolds into .” Exp. Math. 15: 3 (2006), 291–305.
   Web of Science ®Google Scholar
• [Cooper 07] D. Cooper, D. D. Long, and M. B. Thistlethwaite. “Flexing Closed Hyperbolic Manifolds.” Geom. Topol. 11 (2007), 2413–2440.
   Web of Science ®Google Scholar
• [Cox 97] D. Cox, J. Little, and D. O’Shea. Ideals, Varieties, and Algorithms, Undergraduate Texts in Mathematics, 2nd edition. New York: Springer-Verlag, 1997.
   Google Scholar
• [CURVE 14] CURVE. “Computing and Understanding Representation Varieties Efficiently.” http://curve.unhyperbolic.org/, 2014.
   Google Scholar
• [Deraux and Falbel 13] M. Deraux and E. Falbel. “Complex Hyperbolic Geometry of the Complement of the Figure Eight Knot.” arXiv:1303.7096v1. To appear in Geom. Top., 2013.
   Google Scholar
• [Falbel 08] E. Falbel. “A Spherical CR Structure on the Complement of the Figure Eight Knot with Discrete Holonomy.” J. Differ. Geom. 79 (2008), 69–110.
   Web of Science ®Google Scholar
• [Falbel et al. 15a] E. Falbel, P.-V. Koseleff, and F. Rouillier. “Representations of Fundamental Groups of 3-Manifolds Into : Exact Computations in Low Complexity.” Geometriae Dedicata 177: 1 (2015), 229–255.
   Web of Science ®Google Scholar
• [Falbel et al. 15b] E. Falbel, A. Guilloux, P. V. Koseleff, and F. Rouillier. “Maple Worksheet for Computing the Figure Eight Knot Complement Caracter Variety.” https://who.rocq.inria.fr/Fabrice.Rouillier/Web_4_1/4_1_final.html., 2015.
   Google Scholar
• [Garoufalidis 12] S. Garoufalidis, M. Goerner, and C. K. Zickert. “Gluing Equations for -Representations of 3-Manifolds.” arXiv:1207.6711, 2012.
   Google Scholar
• [Garoufalidis et al. 11] S. Garoufalidis, D. Thurston, and C. K. Zickert. The complex volume of -representations of 3-manifolds. arXiv:1111.2828., 2011.
   Google Scholar
• [Guilloux 13] A. Guilloux. “Deformation of Hyperbolic Manifolds in and Discreteness of the Peripheral Representations.” Proc. AMS. To appear, 2013.
   Web of Science ®Google Scholar
• [Heusener 15] M. Heusener, V. Munoz, and J. Porti. “The SL(3,C)-Character Variety of the Figure Eight Knot.” ArXiv e-prints, May2015.
   Google Scholar
• [Lawton 06] S. Lawton. “-Character Varieties and -Structures on a Trinion.” PhD diss., University of Maryland, 2006.
   Google Scholar
• [Lenstra 82] A. Lenstra, H. Lenstra, and L. Lovasz. “Factoring Polynomials with Rational Coefficients.” Math. Annalen 261 (1982), 515–534.
   Web of Science ®Google Scholar
• [Menal-Ferrer and Porti 12] P. Menal-Ferrer and J. Porti. “Local Coordinates for -Character Varieties of Finite Volume Hyperbolic 3-Manifolds.” Ann. Math. Blaise Pascal, 19: 1 (2012), 107–122.
   Google Scholar
• [Mumford 76] D. Mumford. Algebraic Geometry, I. Complex projective varieties, Grundlehren der Mathematischen Wissenschaften, No. 221. Berlin-New York: Springer-Verlag, 1976.
   Google Scholar
• [Ragot 97] J.-F. Ragot. “Sur la factorisation absolue des polynômes.” PhD diss., Université de Limoges, 1997.
   Google Scholar
• [Segerman and Tillmann 11] H. Segerman and S. Tillmann. “Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations.” Contemp. Math. 560 (2011), 85–102.
   Google Scholar
• [Sikora 12] A. S. Sikora. “Character Varieties.” Tran. Am. Math. Soc. 364: 10 (2012), 5173–5208.
   Web of Science ®Google Scholar
• [Sikora 01] Adam S. Sikora. “SLn-Character Varieties as Spaces of Graphs.” Tran. Am. Math. Soc. 353: 7 (2001), 2773–2804.
   Web of Science ®Google Scholar
• [Thurston 80] W. Thurston. “The Geometry and Topology of 3-Manifolds.” (http://library.msri.org/books/gt3m/), 1980.
   Google Scholar
• [Zickert] C. K. Zickert. “Ptolemy Coordinates, Dehn Invariant, and the A-Polynomial.” arXiv:1405.0025.
   Google Scholar