"Kashaev's volume conjecture"의 두 판 사이의 차이

2013년 6월 22일 (토) 04:48 판

The hyperbolic volume of a knot complement can be calculated using the Jones polynimials of the ca
$SU(2)$ connections on $S^3-K$ should be sensitive to the flat $SL_2(C)$ connection defining its hyperbolic structure

1995 Kashaev constructed knot invariants $\langle K \rangle_N$
1997 ?
2001(?) Murakami-Murakami found that $\langle K \rangle_N$ can be obtained from colored Jones polynomial

Zagier Between Number theory and topology.pdf
http://www.math.titech.ac.jp/~Jerome/090210%20workshop.pdf
Hyperbolic volume and the Jones polynomial (PDF), notes from a lecture at MSRI, December 2000. Earlier notes (covering more material) from a lecture series at the Grenoble summer school “Invariants des noeuds et de variétés de dimension 3”, June 1999.
Murakami, Hitoshi. 2010. An Introduction to the Volume Conjecture. 1002.0126 (January 31). http://arxiv.org/abs/1002.0126.
H. Murakami, 2008, An introduction to the volume conjecture and its generalizations
H. Murakami, A quantum introduction to knot theory

Dimofte, Tudor Dan. 2010. “Refined BPS Invariants, Chern-Simons Theory, and the Quantum Dilogarithm”. Phd, California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05142010-131147918.
Generalized volume conjecture and the A-polynomials: The Neumann–Zagier potential function as a classical limit of the partition function , 2007 http://dx.doi.org/10.1016/j.geomphys.2007.03.008
Volume Conjecture and Asymptotic Expansion of q-Series
- Kazuhiro Hikami, Experiment. Math. Volume 12, Number 3 (2003), 319-338
Proof of the volume conjecture for torus knots
- R. M. Kashaev and O. Tirkkonen, 2003
Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
- Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, and Yoshiyuki Yokota, 2002
Hyperbolic Structure Arising from a Knot Invariant, 2001
J.Murakami, H.Murakami, The colored Jones polynomials and the simplicial volume of a knot Acta Math. 186 (2001), 85–104
Yoshiyuki Yokota On the volume conjecture for hyperbolic knots, 2000
R. M. Kashaev The hyperbolic volume of knots from quantum dilogarithm, 1996

@@ 29번째 줄: / 29번째 줄: @@
 ==expositions==
+* Zagier [https://docs.google.com/file/d/0B8XXo8Tve1cxbGQwMUVpQlhlREk/edit Between Number theory and topology.pdf]
 * http://www.math.titech.ac.jp/~Jerome/090210%20workshop.pdf
 * [http://www.math.columbia.edu/%7Edpt/speaking/hypvol.ps Hyperbolic volume and the Jones polynomial] ([http://www.math.columbia.edu/%7Edpt/speaking/hypvol.pdf PDF]), notes from a lecture at MSRI, December 2000. [http://www.math.columbia.edu/%7Edpt/speaking/Grenoble.pdf Earlier notes] (covering more material) from a lecture series at the Grenoble summer school “Invariants des noeuds et de variétés de dimension 3”, June 1999.