"Volume of hyperbolic 3-manifolds"의 두 판 사이의 차이

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==introduction==
  
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* volume is an important invariant of hyperbolic 3-manifold
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* big open problem [[Kashaev's volume conjecture]]
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*  three simple hyperbolic knots
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** <math>4_{1}</math> figure 8 knot
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** <math>5_{2}</math>
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** <math>6_{1}</math>, <math>6_{1}</math>, <math>6_{1}</math>
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* 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==
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* [[Figure eight knot]]
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==other examples==
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* <math>V(4_{1})=2.029883212819\cdots</math>
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* <math>V(5_{2})=2.82812208\cdots</math>
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* <math>V(6_{1})=3.163963228\cdots</math>
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==Chern-Simons invariant==
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* [[Chern-Simons gauge theory and invariant|Chern-Simons theory]]
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==Jones polynomial==
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* 
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==links==
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* [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)]
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==history==
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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==related items==
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==computational resource==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxX3ZsSC04OEUwU0k/edit
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==encyclopedia==
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* http://ko.wikipedia.org/wiki/
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* [http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)]
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* http://en.wikipedia.org/wiki/
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==expositions==
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*  Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf
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==articles==
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* 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.
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* 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.
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* Alexander Goncharov, [http://www.jstor.org/stable/2646189 Volumes of Hyperbolic Manifolds and Mixed Tate Motives], 1999
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* 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.
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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.
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* 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
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* Borel, A. “Commensurability Classes and Volumes of Hyperbolic 3-Manifolds.” Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)
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http://www.numdam.org/numdam-bin/item?ma=211807&id=ASNSP_1981_4_8_1_1_0.
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[[분류:개인노트]]
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[[분류:math and physics]]
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[[분류:Number theory and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q168697 Q168697]
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===Spacy 패턴 목록===
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* [{'LOWER': 'figure'}, {'OP': '*'}, {'LOWER': 'eight'}, {'LEMMA': 'knot'}]
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* [{'LOWER': 'listing'}, {'LOWER': "'s"}, {'LEMMA': 'knot'}]
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* [{'LEMMA': '4_1'}]
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* [{'LEMMA': '4₁'}]
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* [{'LEMMA': '4a_1'}]
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* [{'LOWER': 'figure'}, {'OP': '*'}, {'LEMMA': 'eight'}]

2021년 2월 17일 (수) 02:53 기준 최신판

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



related items

computational resource


encyclopedia




expositions



articles

http://www.numdam.org/numdam-bin/item?ma=211807&id=ASNSP_1981_4_8_1_1_0.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'figure'}, {'OP': '*'}, {'LOWER': 'eight'}, {'LEMMA': 'knot'}]
  • [{'LOWER': 'listing'}, {'LOWER': "'s"}, {'LEMMA': 'knot'}]
  • [{'LEMMA': '4_1'}]
  • [{'LEMMA': '4₁'}]
  • [{'LEMMA': '4a_1'}]
  • [{'LOWER': 'figure'}, {'OP': '*'}, {'LEMMA': 'eight'}]
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