"Knot theory"의 두 판 사이의 차이
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* [[topological quantum field theory(TQFT)]] | * [[topological quantum field theory(TQFT)]] | ||
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| + | ==== 하위페이지 ==== | ||
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| + | * [[Knot theory]]<br> | ||
| + | ** [[hyperbolic knots]]<br> | ||
| + | ** [[Jones polynomials]]<br> | ||
| + | ** [[Kashaev's volume conjecture]]<br> | ||
| + | ** [[knot database]]<br> | ||
| + | *** [[Borromean rings 6 {2}^{3}]]<br> | ||
| + | ** [[knot invariants and exactly solvable models]]<br> | ||
| + | ** [[torus knots]]<br> | ||
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| 139번째 줄: | 156번째 줄: | ||
<h5>articles</h5> | <h5>articles</h5> | ||
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* [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> | ||
** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418 | ** Kashaev, R. M., Modern Phys. Lett. A 10 (1995), 1409–1418 | ||
| 148번째 줄: | 163번째 줄: | ||
* [http://siba2.unile.it/ese/issues/1/19/Notematv9supplp17.pdf Knot and physics]<br> | * [http://siba2.unile.it/ese/issues/1/19/Notematv9supplp17.pdf Knot and physics]<br> | ||
** Kauffman, 1989<br> | ** Kauffman, 1989<br> | ||
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* [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pjm/1102650387 On knot invariants related to some statistical mechanical models.]<br> | * [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pjm/1102650387 On knot invariants related to some statistical mechanical models.]<br> | ||
2010년 11월 6일 (토) 05:12 판
introduction
Given a knot and a rational number one can define a closed three-manifold by Dehn surgery
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
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
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