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In this paper we give an introduction to the volume conjecture and its generalizations.
G. Burde, Darstellungen von Knotengruppen , Math. Ann. 173
1967
Earlier work this paper cites.
G. de Rham, Introduction aux polynômes d’un nœud , Enseignement Math. (2) 13
1968
Earlier work this paper cites.
A. Whittemore, On representations of the group of Listing’s knot by subgroups of SL ( 2 , C ) {\rm SL}(2,\,C) , Proc. Amer. Math. Soc. 40
1973
Earlier work this paper cites.
S.-S. Chern and J. Simons, Characteristic forms and geometric invariants , Ann. of Math. (2) 99
1974
Earlier work this paper cites.
M. Gromov, Volume and bounded cohomology , Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99 (1983)
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.
P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links , Bull. Amer. Math. Soc. (N.S.) 12
1985
Earlier work this paper cites.
C.F. Ho, A new polynomial invariant for knots and links , Abstracts Amer. Math. Soc. 6
1985
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.
R. Brandt, W.B.R. Lickorish, and K. Millett, A polynomial invariant for unoriented knots and links , Invent. Math. 84
1986
Earlier work this paper cites.
M. Culler, Lifting representations to covering groups , Adv. in Math. 59
1986
Earlier work this paper cites.
R. Meyerhoff, Density of the Chern–Simons invariant for hyperbolic 3 3 -manifolds , Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984), Cambridge Univ. Press, Cambridge, 1986, pp. 217–239
1986
Earlier work this paper cites.
L. H. Kauffman, On knots , Annals of Mathematics Studies, vol. 115, Princeton University Press, Princeton, NJ, 1987
1987
Earlier work this paper cites.
by same author, State models and the Jones polynomial , Topology 26
1987
Earlier work this paper cites.
J. H. Przytycki and P. Traczyk, Invariants of links of Conway type , Kobe J. Math. 4
1988
Earlier work this paper cites.
P. Kirk and E. Klassen, Chern-Simons invariants of 3 3 -manifolds and representation spaces of knot groups , Math. Ann. 287
1990
Earlier work this paper cites.
V. A. Vassiliev, Cohomology of knot spaces , Theory of Singularities and Its Applications (V.I. Arnold, ed.), Advances in Soviet Math., vol. 1, Amer. Math. Soc., Providence, 1990
1990
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.
J.S. Birman and X.-S. Lin, Knot polynomials and Vassiliev’s invariants , Invent. Math. 111
1993
Cited alongside, same era.
by same author, 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.
M. Kontsevich, Vassiliev’s knot invariants , I. M. Gel ′
1993
Cited alongside, same era.
T. T. Q. Le, Varieties of representations and their cohomology-jump subvarieties for knot groups. , Russ. Acad. Sci., Sb., Math. 78
1993
Cited alongside, same era.
D. Cooper, M. Culler, H. Gillet, D. D. Long, and P. B. Shalen, Plane curves associated to character varieties of 3 3 -manifolds , Invent. Math. 118
1994
Cited alongside, same era.
H. Murakami, J. Murakami, M. Okamoto, T. Takata, and Y. Yokota, Kashaev’s conjecture and the Chern-Simons invariants of knots and links , Experiment. Math. 11
2002
Later among the works it cites.
W. P. Thurston, The Geometry and Topology of Three-Manifolds , Electronic version 1.1 - March 2002, http://www.msri.org/publications/books/gt3m/
2002
Later among the works it cites.
K. Hikami, Volume conjecture and asymptotic expansion of q q -series , Experiment. Math. 12
2003
Later among the works it cites.
K. Hikami and A. N. Kirillov, Torus knot and minimal model , Phys. Lett. B 575
2003
Later among the works it cites.
by same author, Quantum invariants of 3-manifolds: integrality, splitting, and perturbative expansion , Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three-Manifolds” (Calgary, AB, 1999), vol. 127, 2003, pp. 125–152
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V. G. Turaev, Quantum invariants of knots and 3-manifolds , de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter & Co., Berlin, 1994
1994
Cited alongside, same era.
D. Bar-Natan, On the Vassiliev knot invariant , Topology 34
1995
Cited alongside, same era.
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
Cited alongside, same era.
R. M. Kashaev, A link invariant from quantum dilogarithm , Modern Phys. Lett. A 10
1995
Cited alongside, same era.
C. Kassel, Quantum Groups , Graduate Texts in Mathematics, vol. 155, Springer-Verlag, 1995
1995
Cited alongside, same era.
H. R. Morton, The coloured Jones function and Alexander polynomial for torus knots , Math. Proc. Cambridge Philos. Soc. 117
1995
Cited alongside, same era.
T. Q. T. Le and J. Murakami, The universal Vassiliev-Kontsevich invariant for framed oriented links , Compositio Math. 102
1996
Cited alongside, same era.
2003
Later among the works it cites.
G. Masbaum, Skein-theoretical derivation of some formulas of Habiro , Algebr. Geom. Topol. 3
2003
Later among the works it cites.
by same author, Quantum invariant for torus link and modular forms , Comm. Math. Phys. 246
2004
Later among the works it cites.
M. Khovanov and L. Rozansky, Matrix factorizations and link homology , 2004, arXiv.org:math/0401268
2004
Later among the works it cites.
H. Murakami, Asymptotic behaviors of the colored Jones polynomials of a torus knot , Internat. J. Math. 15
2004
Later among the works it cites.
by same author, Some limits of the colored Jones polynomials of the figure-eight knot , Kyungpook Math. J. 44
2004
Later among the works it cites.
by same author, q q -series and L L -functions related to half-derivatives of the Andrews-Gordon identity , Ramanujan J. 11
2006
Later among the works it cites.
R. van der Veen, Proof of the volume conjecture for Whitehead chains , 2006, arXiv:math/0611181
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.
K. Hikami and H. Murakami, Colored jones polynomials with polynomial growth , 2007, arXiv:0711.2836
2007
Later among the works it cites.
by same author, The colored Jones polynomials and the Alexander polynomial of the figure-eight knot , JP J. Geom. Topol. 2
2007
Later among the works it cites.
by same author, Various generalizations of the volume conjecture , The interaction of analysis and geometry, Contemp. Math., vol. 424, Amer. Math. Soc., Providence, RI, 2007, pp. 165–186
2007
Later among the works it cites.
by same author, A version of the volume conjecture , Adv. Math. 211
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.
2007
Later among the works it cites.