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The volume conjecture states that for a hyperbolic knot K in the three-sphere S^3 the asymptotic growth of the colored Jones polynomial of K is governed by the hyperbolic volume of the knot complement S^3\K.
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H. M. Hilden, M. T. Lozano, and J. M. Montesinos-Amilibia, On volumes and Chern-Simons invariants of geometric 3-manifolds
1996
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R. M. Kashaev, The hyperbolic volume of knots from quantum dilogarithm
1997
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1997
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D. Coulson, O. Goodman, C. Hodgson, and W. Neumann, Computing arithmetic invariants of 3-manifolds
2000
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K. Habiro, On the colored Jones polynomials of some simple links
2000
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2001
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2005
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H. Murakami and Y. Yokota, The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces
2007
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H. Murakami, The colored Jones polynomials and the Alexander polynomial of the figure-eight knot
2007
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2009
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2009
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C. K. Zickert, The Chern-Simons invariant of a representation
2049
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