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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| − | + | ==introduction</h5> | |
* [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)] | * [http://pythagoras0.springnote.com/pages/5098745 매듭이론 (knot theory)] | ||
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| − | + | ==knot diagram</h5> | |
* projection to two dimensional space | * projection to two dimensional space | ||
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| − | + | ==Kauffman's principle</h5> | |
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| − | + | ==knot invariants</h5> | |
* Alexander-Conway polynomial | * Alexander-Conway polynomial | ||
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| − | + | ==Jones polynomial</h5> | |
* Kauffman bracket | * Kauffman bracket | ||
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| − | + | ==2+1 dimensional TQFT</h5> | |
* [[topological quantum field theory(TQFT)]] | * [[topological quantum field theory(TQFT)]] | ||
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| − | + | ==knot and QFT</h5> | |
* [[knot and quantum field theory]] | * [[knot and quantum field theory]] | ||
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| − | + | ==history</h5> | |
* 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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| − | + | ==related items</h5> | |
* [[volume of hyperbolic threefolds and L-values|volume of hyperbolic 3-manifolds and L-values]] | * [[volume of hyperbolic threefolds and L-values|volume of hyperbolic 3-manifolds and L-values]] | ||
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| − | + | ==books</h5> | |
* The Geometry and Physics of Knots<br> | * The Geometry and Physics of Knots<br> | ||
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| − | + | ==encyclopedia[http://ko.wikipedia.org/wiki/%EB%A7%A4%EB%93%AD%EC%9D%B4%EB%A1%A0 ]</h5> | |
* http://en.wikipedia.org/wiki/knot_theory | * http://en.wikipedia.org/wiki/knot_theory | ||
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| − | + | ==question and answers(Math Overflow)</h5> | |
* http://mathoverflow.net/search?q=knot+quantum | * http://mathoverflow.net/search?q=knot+quantum | ||
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| − | + | ==blogs</h5> | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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| − | + | ==articles</h5> | |
* [http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm]<br> | * [http://dx.doi.org/10.1142/S0217732395001526 A link invariant from quantum dilogarithm]<br> | ||
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| − | + | ==experts on the field</h5> | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | + | ==TeX </h5> | |
2012년 10월 28일 (일) 13:11 판
==introduction
Given a knot and a rational number one can define a closed three-manifold by Dehn surgery
- Knot complements and 3-manifolds
- a knot K is either hyperbolic or a torus knot or a satellite knot
==knot diagram
- projection to two dimensional space
==Kauffman's principle
==knot invariants
- Alexander-Conway polynomial
- Jones polynomial
- Vassiliev invariants
- define them recursively using the skein relation
- Reidemeister's theorem is used to prove that they are knot invariants
- The puzzle on the mathematical side was that these objects are invariants of a three dimensional situation, but one did not have an intrinsically three dimensional definition.
- There were many elegant definitions of the knot polynomials, but they all involved looking in some way at a two dimensional projection or slicing of the knot, giving a two dimensional algorithm for computation, and proving that the result is independent of the chosen projection.
- This is analogous to studying a physical theory that is in fact relativistic but in which one does not know of a manifestly relativistic formulation - like quantum electrodynamics in the 1930's.
==Jones polynomial
- Kauffman bracket
- colored Jones polynomial
- Hecke algebra
- Jones polynomials and \(U_q[\mathfrak{sl}(2)]\)
Knot theory, statistical mechanics and quantum groups
- Knot Theory and Statistical Mechanics
- using the Boltzmann weights from the various exactly solvable models, we can discover an infinite series of invariants of knots
- so the problem is to find a nice set of Boltzmann weights which give non-trivial invariants
==2+1 dimensional TQFT
==knot and QFT
하위페이지
- Knot theory
- hyperbolic knots
- Jones polynomials
- Kashaev's volume conjecture
- knot database
- [[Borromean rings 6 {2}^{3}]]
- [[Borromean rings 6 {2}^{3}]]
- knot invariants and exactly solvable models
- torus knots
- hyperbolic knots
==history
==related items
==books
- The Geometry and Physics of Knots
- Atiyah, Michael
- 찾아볼 수학책
- http://gigapedia.info/1/atiyah
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
==encyclopedia[1]
- http://en.wikipedia.org/wiki/knot_theory
- http://en.wikipedia.org/wiki/List_of_knot_theory_topics
- http://en.wikipedia.org/wiki/Link_(knot_theory)
- http://en.wikipedia.org/wiki/Reidemeister_move
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
==question and answers(Math Overflow)
- http://mathoverflow.net/search?q=knot+quantum
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
==blogs
- 구글 블로그 검색
==articles
- A link invariant from quantum dilogarithm
- Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418
- Knot theory and statistical mechanics
- Richard Altendorfer
- http://www.bkfc.net/altendor/KnotTheoryAndStatisticalMechanics.pdf
- Knot and physics
- Kauffman, 1989
- Kauffman, 1989
- On knot invariants related to some statistical mechanical models.
- V. F. R. Jones, 1989
- The Yang-Baxter equation and invariants of links
- Turaev, 1988
- An Introduction to Knot Theory
- Richard Altendorfer
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- 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/
==experts on the field
==TeX