"3-manifolds and their invariants"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 three-manifolds and their invariants로 바꾸었습니다.) |
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| 22번째 줄: | 22번째 줄: | ||
* Prove<br><math>\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=\frac{2}{\sqrt{7}}(Cl(2\pi /7})+Cl(4\pi/7})-Cl(6\pi/7}))</math><br> | * Prove<br><math>\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=\frac{2}{\sqrt{7}}(Cl(2\pi /7})+Cl(4\pi/7})-Cl(6\pi/7}))</math><br> | ||
| − | * [[ | + | * [[a log tangent integral|problems in integrals]]<br> |
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| + | <h5 style="line-height: 2em; margin: 0px;">Reshetikihn, Turaev</h5> | ||
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| 55번째 줄: | 63번째 줄: | ||
** [[triangulations and Bloch group]]<br> | ** [[triangulations and Bloch group]]<br> | ||
** [[volume of hyperbolic threefolds and L-values|volume of hyperbolic 3-manifolds and L-values]]<br> | ** [[volume of hyperbolic threefolds and L-values|volume of hyperbolic 3-manifolds and L-values]]<br> | ||
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| 98번째 줄: | 104번째 줄: | ||
* [http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links]<br> | * [http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links]<br> | ||
** J.M. Borwein, D.J. Broadhurst, 1998 | ** J.M. Borwein, D.J. Broadhurst, 1998 | ||
| + | * Three-manifolds and the Temperley-Lieb algebra<br> | ||
| + | ** W. B. R. Lickorish, 1991 | ||
* [[2010년 books and articles|논문정리]] | * [[2010년 books and articles|논문정리]] | ||
2010년 7월 17일 (토) 15:23 판
introduction
- volume of knot complements
- Chern-Simons invariant of manifolds
Volume of knot complement
- KnotData[]
KnotData["FigureEight", "HyperbolicVolume"]
N[%, 20]
- Dedekind zeta funciton evaluated at 2 gives a number related to volume of 3-manifold
- Bloch-Wigner dilogarithm is involved
an open problem
- Prove
\(\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=\frac{2}{\sqrt{7}}(Cl(2\pi /7})+Cl(4\pi/7})-Cl(6\pi/7}))\) - problems in integrals
Reshetikihn, Turaev
software
history
하위페이지
encyclopedia
-
- http://ko.wikipedia.org/wiki/[1]
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
[[4909919|]]
articles
- Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links
- J.M. Borwein, D.J. Broadhurst, 1998
- Three-manifolds and the Temperley-Lieb algebra
- W. B. R. Lickorish, 1991
- 논문정리
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[2]
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- 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=
- http://dx.doi.org/10.1063/1.3085764
question and answers(Math Overflow)
blogs
experts on the field