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

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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">introduction</h5>
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==introduction==
  
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* hyperbolic 3-manifold : figure 8 knot complement<br>
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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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<h5 style="line-height: 2em; margin: 0px;">volume </h5>
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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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* 2.02988321281930725<br><math>V=\frac{9\sqrt{3}}{\pi^2}\zeta_{\mathbb{Q}(\sqrt{-3})}(2)=3D(e^{\frac{2i\pi}{3}})=2D(e^{\frac{i\pi}{3}})=2.029883212819\cdots</math><br> where D is [http://pythagoras0.springnote.com/pages/4633853 Bloch-Wigner dilogarithm].<br>
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*  what is <math>\zeta_{\mathbb{Q}(\sqrt{-3})}(2)</math>? numrically 1.285190955484149<br>
 
  
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# L[x_] := Im[PolyLog[2, x]] + 1/2 Log[Abs[x]] Arg[1 - x]<br> f[x_, y_] :=<br>  L[x] + L[1 - x*y] + L[y] + L[(1 - y)/(1 - x*y)] + L[(1 - x)/(1 - x*y)]<br> Print["five term relation"]<br> Table[f[i, j], {i, 0.1, 0.9, 0.1}, {j, 0.1, 0.9, 0.1}] // TableForm<br> N[3 L[Exp[2 I*Pi/3]], 20]<br> N[2 L[Exp[I*Pi/3]], 20]<br> N[3 (L[Exp[2 I*Pi/3]] - L[Exp[4 I*Pi/3]])/2, 20]<br> N[Pi^2*L[Exp[2 I*Pi/3]]/(3 Sqrt[3]), 20]<br>
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==Chern-Simons invariant==
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<h5>Chern-Simons invariant</h5>
 
  
 
* [[Chern-Simons gauge theory and invariant|Chern-Simons theory]]
 
* [[Chern-Simons gauge theory and invariant|Chern-Simons theory]]
  
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<h5>Jones polynomial</h5>
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==Jones polynomial==
  
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*  
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*
  
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<h5>links</h5>
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==links==
  
 
* [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)]
 
* [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)]
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">history</h5>
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==history==
  
 
* 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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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items</h5>
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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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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
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==encyclopedia==
  
 
* http://ko.wikipedia.org/wiki/
 
* 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)]
 
* http://en.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books</h5>
 
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* [[2010년 books and articles]]<br>
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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[[4909919|]]
 
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5>
 
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* [http://www.jstor.org/stable/2646189 Volumes of Hyperbolic Manifolds and Mixed Tate Motives]<br>
 
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** Alexander Goncharov, <cite>[http://www.jstor.org/action/showPublication?journalCode=jamermathsoci Journal of the American Mathematical Society]</cite>, Vol. 12, No. 2 (Apr., 1999), pp. 569-618
 
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* [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions]<br>
 
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** Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
 
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*  Commensurability classes and volumes of hyperbolic 3-manifolds<br>
 
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** A. Borel, Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)
 
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* [[2010년 books and articles|논문정리]]
 
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* http://www.ams.org/mathscinet
 
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* http://www.zentralblatt-math.org/zmath/en/
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html][http://www.ams.org/mathscinet ]
 
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
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* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
 
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* http://dx.doi.org/10.1007/s100529900935
 
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">question and answers(Math Overflow)</h5>
 
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* http://mathoverflow.net/search?q=
 
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* http://mathoverflow.net/search?q=
 
  
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">blogs</h5>
 
  
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* 구글 블로그 검색<br>
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** http://blogsearch.google.com/blogsearch?q=
 
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** http://blogsearch.google.com/blogsearch?q=
 
  
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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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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">experts on the field</h5>
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* http://arxiv.org/
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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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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">links</h5>
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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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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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==메타데이터==
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
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===위키데이터===
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
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* ID :  [https://www.wikidata.org/wiki/Q168697 Q168697]
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* http://functions.wolfram.com/
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===Spacy 패턴 목록===
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*
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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'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Volume_of_hyperbolic_3-manifolds&oldid=51851"