"Kashaev's volume conjecture"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| − | * 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 | + | * $SU(2)$ connections on $S^3-K$ should be sensitive to the flat $SL_2(C)$ connection defining its hyperbolic structure |
| 30번째 줄: | 30번째 줄: | ||
==expositions== | ==expositions== | ||
* http://www.math.titech.ac.jp/~Jerome/090210%20workshop.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. | + | * [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. |
| − | * Murakami, Hitoshi. 2010. An Introduction to the Volume Conjecture. 1002.0126 (January 31). http://arxiv.org/abs/1002.0126. | + | * 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, 2008, An introduction to the volume conjecture and its generalizations | ||
| 40번째 줄: | 40번째 줄: | ||
* 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 | * 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 | ||
| − | * [http://projecteuclid.org/euclid.em/1087329235 Volume Conjecture and Asymptotic Expansion of q-Series] | + | * [http://projecteuclid.org/euclid.em/1087329235 Volume Conjecture and Asymptotic Expansion of q-Series] |
** Kazuhiro Hikami, Experiment. Math. Volume 12, Number 3 (2003), 319-338 | ** Kazuhiro Hikami, Experiment. Math. Volume 12, Number 3 (2003), 319-338 | ||
| − | * [http://dx.doi.org/10.1023/A:1022608131142 Proof of the volume conjecture for torus knots] | + | * [http://dx.doi.org/10.1023/A:1022608131142 Proof of the volume conjecture for torus knots] |
** R. M. Kashaev and O. Tirkkonen, 2003 | ** R. M. Kashaev and O. Tirkkonen, 2003 | ||
| − | * [http://projecteuclid.org/euclid.em/1057777432 Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links] | + | * [http://projecteuclid.org/euclid.em/1057777432 Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links] |
** 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] | + | * [http://dx.doi.org/10.1007/BF02392716 The colored Jones polynomials and the simplicial volume of a knot] |
** J.Murakami, H.Murakami,, Acta Math. 186 (2001), 85–104 | ** J.Murakami, H.Murakami,, Acta Math. 186 (2001), 85–104 | ||
| − | * [http://arxiv.org/abs/math/0009165 On the volume conjecture for hyperbolic knots] | + | * [http://arxiv.org/abs/math/0009165 On the volume conjecture for hyperbolic knots] |
** Yoshiyuki Yokota, 2000 | ** Yoshiyuki Yokota, 2000 | ||
| − | * [http://dx.doi.org/10.1023/A:1007364912784 The hyperbolic volume of knots from quantum dilogarithm] | + | * [http://dx.doi.org/10.1023/A:1007364912784 The hyperbolic volume of knots from quantum dilogarithm] |
** R. M. Kashaev, 1996 | ** R. M. Kashaev, 1996 | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 4월 24일 (수) 02:05 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
- 1997 ?
- 2001(?) Murakami
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
- The colored Jones polynomials and the simplicial volume of a knot
- J.Murakami, H.Murakami,, Acta Math. 186 (2001), 85–104
- On the volume conjecture for hyperbolic knots
- Yoshiyuki Yokota, 2000
- The hyperbolic volume of knots from quantum dilogarithm
- R. M. Kashaev, 1996