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* 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. | * 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], Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월 | * 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 | ||
| − | * A. | + | * 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. | |
2015년 1월 17일 (토) 18:44 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
- \(5_{2}\)
- \(6_{1}\), \(6_{1}\), \(6_{1}\)
- \(4_{1}\) figure 8 knot
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
- 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.