"Volume of hyperbolic 3-manifolds"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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* volume is an important invariant of hyperbolic 3-manifold | * volume is an important invariant of hyperbolic 3-manifold | ||
* big open problem [[Kashaev's volume conjecture]] | * big open problem [[Kashaev's volume conjecture]] | ||
| − | * three simple hyperbolic knots | + | * three simple hyperbolic knots |
| − | ** <math>4_{1}</math> | + | ** <math>4_{1}</math> figure 8 knot |
| − | ** <math>5_{2}</math | + | ** <math>5_{2}</math> |
| − | ** <math>6_{1}</math>, | + | ** <math>6_{1}</math>, <math>6_{1}</math>, <math>6_{1}</math> |
| − | + | * A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus | |
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==volume of figure eight knot complement== | ==volume of figure eight knot complement== | ||
* [[Figure eight knot]] | * [[Figure eight knot]] | ||
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==other examples== | ==other examples== | ||
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* <math>V(6_{1})=3.163963228\cdots</math> | * <math>V(6_{1})=3.163963228\cdots</math> | ||
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==Chern-Simons invariant== | ==Chern-Simons invariant== | ||
| 34번째 줄: | 31번째 줄: | ||
* [[Chern-Simons gauge theory and invariant|Chern-Simons theory]] | * [[Chern-Simons gauge theory and invariant|Chern-Simons theory]] | ||
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==Jones polynomial== | ==Jones polynomial== | ||
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==links== | ==links== | ||
| 50번째 줄: | 47번째 줄: | ||
* [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)] | * [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)] | ||
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==history== | ==history== | ||
| 58번째 줄: | 55번째 줄: | ||
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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==related items== | ==related items== | ||
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==computational resource== | ==computational resource== | ||
* https://docs.google.com/file/d/0B8XXo8Tve1cxX3ZsSC04OEUwU0k/edit | * https://docs.google.com/file/d/0B8XXo8Tve1cxX3ZsSC04OEUwU0k/edit | ||
| 80번째 줄: | 77번째 줄: | ||
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==expositions== | ==expositions== | ||
| 86번째 줄: | 83번째 줄: | ||
* Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf<br> | * Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf<br> | ||
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==articles== | ==articles== | ||
| + | * Purcell, Jessica S., and Alexander Zupan. “Independence of Volume and Genus $g$ Bridge Numbers.” arXiv:1512.03869 [math], December 11, 2015. http://arxiv.org/abs/1512.03869. | ||
* Le, Thang. “Growth of Homology Torsion in Finite Coverings and Hyperbolic Volume.” arXiv:1412.7758 [math], December 24, 2014. http://arxiv.org/abs/1412.7758. | * Le, Thang. “Growth of Homology Torsion in Finite Coverings and Hyperbolic Volume.” arXiv:1412.7758 [math], December 24, 2014. http://arxiv.org/abs/1412.7758. | ||
* Alexander Goncharov, [http://www.jstor.org/stable/2646189 Volumes of Hyperbolic Manifolds and Mixed Tate Motives], 1999 | * Alexander Goncharov, [http://www.jstor.org/stable/2646189 Volumes of Hyperbolic Manifolds and Mixed Tate Motives], 1999 | ||
| − | * Gliozzi, F., and R. Tateo. 1995. Thermodynamic Bethe Ansatz and Threefold Triangulations. hep-th/9505102 (May 17). doi:doi:[http://dx.doi.org/10.1142/S0217751X96001905 10.1142/S0217751X96001905]. http://arxiv.org/abs/hep-th/9505102. | + | * Gliozzi, F., and R. Tateo. 1995. Thermodynamic Bethe Ansatz and Threefold Triangulations. hep-th/9505102 (May 17). doi:doi:[http://dx.doi.org/10.1142/S0217751X96001905 10.1142/S0217751X96001905]. http://arxiv.org/abs/hep-th/9505102. |
| − | * Adams, C., Hildebrand, M. | + | * Adams, C., Hildebrand, M. and Weeks, J., [http://www.jstor.org/stable/2001854 Hyperbolic invariants of knots and links], Trans. Amer.Math. Soc. 1 (1991), 1–56. |
| − | * Don Zagier, [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions], | + | * Don Zagier, [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions], Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월 |
* Borel, A. “Commensurability Classes and Volumes of Hyperbolic 3-Manifolds.” Ann. Sc. Norm. Super. Pisa8, 1–33 (1981) | * Borel, A. “Commensurability Classes and Volumes of Hyperbolic 3-Manifolds.” Ann. Sc. Norm. Super. Pisa8, 1–33 (1981) | ||
http://www.numdam.org/numdam-bin/item?ma=211807&id=ASNSP_1981_4_8_1_1_0. | http://www.numdam.org/numdam-bin/item?ma=211807&id=ASNSP_1981_4_8_1_1_0. | ||
2015년 12월 18일 (금) 22:56 판
introduction
- volume is an important invariant of hyperbolic 3-manifold
- big open problem Kashaev's volume conjecture
- three simple hyperbolic knots
- \(4_{1}\) figure 8 knot
- \(5_{2}\)
- \(6_{1}\), \(6_{1}\), \(6_{1}\)
- A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus
volume of figure eight knot complement
other examples
- \(V(4_{1})=2.029883212819\cdots\)
- \(V(5_{2})=2.82812208\cdots\)
- \(V(6_{1})=3.163963228\cdots\)
Chern-Simons invariant
Jones polynomial
links
history
computational resource
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)
- http://en.wikipedia.org/wiki/
expositions
- Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf
articles
- Purcell, Jessica S., and Alexander Zupan. “Independence of Volume and Genus $g$ Bridge Numbers.” arXiv:1512.03869 [math], December 11, 2015. http://arxiv.org/abs/1512.03869.
- Le, Thang. “Growth of Homology Torsion in Finite Coverings and Hyperbolic Volume.” arXiv:1412.7758 [math], December 24, 2014. http://arxiv.org/abs/1412.7758.
- Alexander Goncharov, Volumes of Hyperbolic Manifolds and Mixed Tate Motives, 1999
- Gliozzi, F., and R. Tateo. 1995. Thermodynamic Bethe Ansatz and Threefold Triangulations. hep-th/9505102 (May 17). doi:doi:10.1142/S0217751X96001905. http://arxiv.org/abs/hep-th/9505102.
- Adams, C., Hildebrand, M. and Weeks, J., Hyperbolic invariants of knots and links, Trans. Amer.Math. Soc. 1 (1991), 1–56.
- Don Zagier, Hyperbolic manifolds and special values of Dedekind zeta-functions, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
- Borel, A. “Commensurability Classes and Volumes of Hyperbolic 3-Manifolds.” Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)
http://www.numdam.org/numdam-bin/item?ma=211807&id=ASNSP_1981_4_8_1_1_0.