"Kashaev's volume conjecture"의 두 판 사이의 차이
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* The hyperbolic volume of a knot complement can be calculated using the Jones polynimials of the ca | * 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 | * $SU(2)$ connections on $S^3-K$ should be sensitive to the flat $SL_2(C)$ connection defining its hyperbolic structure | ||
| + | |||
| + | |||
| + | ==examples== | ||
| + | * $4_1$ | ||
| + | * $5_2$ | ||
| + | * $6_1$ | ||
2013년 6월 22일 (토) 04:51 판
introduction
- 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
examples
- $4_1$
- $5_2$
- $6_1$
history
- 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
- complex Chern-Simons theory
- quantum dilogarithm
- quantum modular forms
- Volume of hyperbolic threefolds and L-values
computational resource
encyclopedia
expositions
- 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
articles
- 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