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We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial.
W. Franz, Über die Torsion einer Überdeckung. , J. Reine Angew. Math. 173
1935
Earlier work this paper cites.
K. Reidemeister, Homotopieringe und Linsenräume. , Abh. Math. Semin. Hamb. Univ. 11
1935
Earlier work this paper cites.
G. de Rham, Sur les nouveaux invariants topologiques de M. Reidemeister. , Rec. Math. Moscou, n. Ser. 1
1936
Earlier work this paper cites.
J. Milnor, A duality theorem for Reidemeister torsion , Ann. of Math. (2) 76
1962
Earlier work this paper cites.
W. H. Jaco and P. B. Shalen, Seifert fibered spaces in 3 3 -manifolds , Mem. Amer. Math. Soc. 21
1979
Earlier work this paper cites.
K. Johannson, Homotopy equivalences of 3 3 -manifolds with boundaries , Lecture Notes in Mathematics, vol. 761, Springer, Berlin, 1979. MR 82c:57005
1979
Earlier work this paper cites.
M. Culler and P. B. Shalen, Varieties of group representations and splittings of 3 3 -manifolds , Ann. of Math. (2) 117
1983
Earlier work this paper cites.
M. Gromov, Volume and bounded cohomology , Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99 (1983). MR 84h:53053
1983
Earlier work this paper cites.
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.
V. G. Turaev, Reidemeister torsion in knot theory , Uspekhi Mat. Nauk 41
1986
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
Cited alongside, same era.
E. Witten, Quantum field theory and the Jones polynomial , Comm. Math. Phys. 121
1989
Cited alongside, same era.
E. P. Klassen, Representations of knot groups in SU ( 2 ) {\rm SU}(2) , Trans. Amer. Math. Soc. 326
1991
Cited alongside, same era.
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
Cited alongside, same era.
by same author, Quantum invariants of knots and 3-manifolds , de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter & Co., Berlin, 1994. MR MR1292673 (95k:57014)
1994
Cited alongside, same era.
K. Hikami and A. N. Kirillov, Torus knot and minimal model , Phys. Lett. B 575
2003
Later among the works it cites.
K. Hikami, Quantum invariant for torus link and modular forms , Comm. Math. Phys. 246
2004
Later among the works it cites.
by same author, Asymptotic behaviors of the colored Jones polynomials of a torus knot , Internat. J. Math. 15
2004
Later among the works it cites.
J. Dubois, Non abelian twisted Reidemeister torsion for fibered knots , Canad. Math. Bull. 49
2006
Later among the works it cites.
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
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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.
R. M. Kashaev and O. Tirkkonen, A proof of the volume conjecture on torus knots , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269
2000
Cited alongside, same era.
H. Murakami, The asymptotic behavior of the colored Jones function of a knot and its volume , Proceedings of ‘Art of Low Dimensional Topology VI’ (T. Kohno, ed.), January 2000, pp. 87–96
2000
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.
2007
Later among the works it cites.
2007
Later among the works it cites.
K. Hikami and H. Murakami, Colored Jones polynomials with polynomial growth , Commun. Contemp. Math. 10
2008
Later among the works it cites.
by same author, An introduction to the volume conjecture and its generalizations , Acta Math. Vietnam. 33
2008
Later among the works it cites.
R. van der Veen, Proof of the volume conjecture for Whitehead chains , Acta Math. Vietnam. 33
2008
Later among the works it cites.
J. Dubois, V. Huynh, and Y. Yamaguchi, Non-abelian Reidemeister torsion for twist knots , J. Knot Theory Ramifications 18
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.