"Kashaev's volume conjecture"의 두 판 사이의 차이
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| 6번째 줄: | 6번째 줄: | ||
==history== | ==history== | ||
| − | * | + | * 1995 Kashaev constructed knot invariants $\langle K \rangle_N$ |
| − | * | + | * 1997 ? |
| − | * 2001(?) Murakami | + | * 2001(?) Murakami-Murakami found that $\langle K \rangle_N$ can be obtained from colored Jones polynomial |
| 48번째 줄: | 48번째 줄: | ||
** Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, and Yoshiyuki Yokota, 2002 | ** Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, and Yoshiyuki Yokota, 2002 | ||
* [http://arxiv.org/abs/math-ph/0105039 Hyperbolic Structure Arising from a Knot Invariant], 2001 | * [http://arxiv.org/abs/math-ph/0105039 Hyperbolic Structure Arising from a Knot Invariant], 2001 | ||
| − | * [http://dx.doi.org/10.1007/BF02392716 The colored Jones polynomials and the simplicial volume of a knot] | + | * J.Murakami, H.Murakami, [http://dx.doi.org/10.1007/BF02392716 The colored Jones polynomials and the simplicial volume of a knot] Acta Math. 186 (2001), 85–104 |
| − | |||
| − | * [http://arxiv.org/abs/math/0009165 On the volume conjecture for hyperbolic knots] | + | * Yoshiyuki Yokota [http://arxiv.org/abs/math/0009165 On the volume conjecture for hyperbolic knots], 2000 |
| − | + | * R. M. Kashaev [http://dx.doi.org/10.1023/A:1007364912784 The hyperbolic volume of knots from quantum dilogarithm], 1996 | |
| − | |||
| − | * [http://dx.doi.org/10.1023/A:1007364912784 The hyperbolic volume of knots from quantum dilogarithm] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:TQFT]] | [[분류:TQFT]] | ||
2013년 5월 30일 (목) 07:26 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
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
computational resource
encyclopedia
expositions
- 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
- 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