Volume conjecture links and notes (under construction)
General:
A list of knots and links for which the volume conjecture has been settled
Hyperbolic
volume and the Jones Polynomial Dylan Thurston. Short account of the volume conjecture.
Dylan Thurston's Notes on
the volume conjecture from a lecture series at the Grenoble summer school
“Invariants des noeuds et de variétés de dimension 3”, June 1999.
A quantum introduction to knot theory H. Murakami introduction to the volume
conjecture.
The colored Jones
polynomials and the simplicial volume of a knot H Murakami, J. Murakami
The hyperbolic volume of
knots from quantum dilogarithm R. Kashaev This is the first article on the
volume conjecture.
Experiments:
Kashaev's conjecture
and the Chern-Simons invariants of knots and links Murakami, Murakami,
Takata, Okamoto, Yokota
Experimental evidence for the
Volume Conjecture for the simplest hyperbolic non-2-bridge knot S.
Garoufalidis
Actual computation for the complexified hyperbolic volume conjecture J.
Murakami
Relationship between the Jones polynomial of a knot at -1 and the hyperbolic
volume its complement N. Dunfield
Twist knots:
The
colored Jones polynomial and the A-Polynomial for twist knots T. Takata
Asymptotics of the Colored
Jones Polynomial and the A-Polynomial K. Hikami
The C-polynomial
of a knot S. Garoufalidis, X. Sun
Kauffman bracket skein module of a twist knot exterior D. Bullock, W. Lo
Faro
Asymptotics of q-difference
equations S. Garoufalidis, S. Geronimo
Torus knots:
Proof of the volume conjecture
for torus knots R. M. Kashaev, O. Tirkkonen
On the asymptotic
expansion of the colored Jones polynomial for torus knots R. Kashaev
Proof of the volume conjecture
for Whitehead doubles of a family of torus knots H. Zheng
Volume conjecture and asymptotic expansion of q-series K. Hikami
Difference
equation of the colored Jones polynomial for torus knot K. Hikami
Torus knot and Minimal model
K. Hikami, A. Kirillov
Asymptiotic
behaviors of the colored Jones polynomials of a torus knot H. Murakami
A cabling formula for the
colored Jones polynomial R. van der Veen
Figure-eight knot:
Asymptotics of the
quantum invariants for surgeries on the figure 8 knot , J.E. Andersen, S. K.
Hansen
Some limits of the
colored Jones polynomials of the figure-eight knot H. Murakami
The colored
Jones polynomials of the figure-eight knot and the volumes of three-manifolds
obtained by Dehn surgeries H. Murakami
The colored Jones
polynomials of the figure-eight knot and its Dehn surgery spaces H. Murakami
Generalized volume conjecture:
Three-Dimensional Quantum
Gravity, Chern-Simons Theory, and the A-Polynomial S. Gukov
Exact Results for Perturbative
Chern-Simons Theory with Complex Gauge Group, Dimofte, Gukov, Lenells,
Zagier
An introduction to the volume
conjecture and its generalizations H. Murakami
A version of
the volume conjecture H. Murakami
Generalized volume conjecture and the A-polynomials K. Hikami
$SL_2(\mathbb{C})$-Character
Variety of a Hyperbolic Link and Regulator W. Li, Q. Wang
A-polynomial:
Plane
Curves Associated to Character Varieties of 3-Manifolds Cooper,
Culler,Gillet, Long, Shalen
Finding a General Form for the A-Polynomial of Twist Knots I. Lankham
AJ-conjecture:
The Colored Jones Polynomial and the A-Polynomial of Knots T. Le
Quantum hyperbolic invariants:
Quantum hyperbolic geometry
S. Baseilhac, R. Benedetti
Quantum
hyperbolic invariants of links: semi-classical triviality versus Jones-Kashaev
invariants S. Baseilhac, R. Benedetti
String Theory:
The Volume Conjecture and Topological Strings R.Dijkgraaf, H. Fuji
Colored Jones polynomial:
Computation of the colored Jones of some simple links, K. Habiro