"Volume of hyperbolic 3-manifolds"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| 81번째 줄: | 81번째 줄: | ||
==expositions== | ==expositions== | ||
| − | * Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf | + | * Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf |
| 88번째 줄: | 88번째 줄: | ||
==articles== | ==articles== | ||
| − | * Purcell, Jessica S., and Alexander Zupan. “Independence of Volume and Genus | + | * Purcell, Jessica S., and Alexander Zupan. “Independence of Volume and Genus <math>g</math> 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 | ||
2020년 11월 13일 (금) 07:23 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.