Fetching the paper…
Reading the bibliography…
We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the fundamental group of the knot complement to the two-dimensional complex special linear group.
R. Riley, Nonabelian representations of 2 2 -bridge knot groups , Quart. J. Math. Oxford Ser. (2) 35
1984
Earlier work this paper cites.
V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras , Bull. Amer. Math. Soc. (N.S.) 12
1985
Earlier work this paper cites.
W. D. Neumann and D. Zagier, Volumes of hyperbolic three-manifolds , Topology 24
1985
Earlier work this paper cites.
T. Yoshida, The η \eta -invariant of hyperbolic 3 3 -manifolds , Invent. Math. 81
1985
Earlier work this paper cites.
J. E. Marsden and M. J. Hoffman, Basic complex analysis , W. H. Freeman and Company, New York, 1987. MR 88m:30001
1987
Earlier work this paper cites.
E. P. Klassen, Representations of knot groups in SU ( 2 ) {\rm SU}(2) , Trans. Amer. Math. Soc. 326
1991
Earlier work this paper cites.
P. Kirk and E. Klassen, Chern-Simons invariants of 3 3 -manifolds decomposed along tori and the circle bundle over the representation space of T 2 {T}^{2} , Comm. Math. Phys. 153
1993
Earlier work this paper cites.
L. D. Faddeev, Discrete Heisenberg-Weyl group and modular group , Lett. Math. Phys. 34
1995
Earlier work this paper cites.
H. Hilden, M. Lozano, and J. M. Montesinos-Amilibia, On a remarkable polyhedron geometrizing the figure eight knot cone manifolds , J. Math. Sci. Univ. Tokyo 2
1995
Earlier work this paper cites.
R. M. Kashaev, A link invariant from quantum dilogarithm , Modern Phys. Lett. A 10
1995
Cited alongside, same era.
by same author, The hyperbolic volume of knots from the quantum dilogarithm , Lett. Math. Phys. 39
1997
Cited alongside, same era.
J. Porti, Torsion de Reidemeister pour les variétés hyperboliques , Mem. Amer. Math. Soc. 128
1997
Cited alongside, same era.
H. Murakami and J. Murakami, The colored Jones polynomials and the simplicial volume of a knot , Acta Math. 186
2001
Cited alongside, same era.
W. P. Thurston, The Geometry and Topology of Three-Manifolds , Electronic version 1.1 - March 2002, http://www.msri.org/publications/books/gt3m/
2002
Cited alongside, same era.
G. Masbaum, Skein-theoretical derivation of some formulas of Habiro , Algebr. Geom. Topol. 3
J. Dubois and R. M. Kashaev, On the asymptotic expansion of the colored jones polynomial for torus knots , Math. Ann. 339
2007
Later among the works it cites.
H. Murakami and Y. Yokota, The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces , J. Reine Angew. Math. 607
2007
Later among the works it cites.
S. Gukov and H. Murakami, S L ( 2 , 𝐂 ) SL(2,\mathbf{C}) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial , Modular Forms and String Duality (N. Yui, H. Verrill, and C.F. Doran, eds.), Fields Inst. Comm., vol. 54, Amer. Math. Soc. and Fields Inst., 2008, pp. 261–278
2008
Later among the works it cites.
H. Murakami, An introduction to the volume conjecture and its generalizations , Acta Math. Vietnam. 33
2008
Later among the works it cites.
T. Dimofte, S. Gukov, J. Lenells, and D. Zagier, Exact results for perturbative Chern-Simons theory with complex gauge group , Commun. Number Theory Phys. 3
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2003
Cited alongside, same era.
S. Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial , Comm. Math. Phys. 255
2005
Cited alongside, same era.
J. E. Andersen and S. K. Hansen, Asymptotics of the quantum invariants for surgeries on the figure 8 knot , J. Knot Theory Ramifications 15
2006
Cited alongside, same era.
J. Dubois, Non abelian twisted Reidemeister torsion for fibered knots , Canad. Math. Bull. 49
2006
Cited alongside, same era.
2009
Later among the works it cites.
V. Muñoz, The SL ( 2 , ℂ ) {\rm SL}(2,\mathbb{C}) -character varieties of torus knots , Rev. Mat. Complut. 22
2009
Later among the works it cites.
2010
Later among the works it cites.
2010
Later among the works it cites.
by same author, An introduction to the volume conjecture , to appear in Contemporary Mathematics ”Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory”, arXiv:1002:0126, 2010
2010
Later among the works it cites.