"3-manifolds and their invariants"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 8번째 줄: | 8번째 줄: | ||
* maps between aspherical 3 manifolds | * maps between aspherical 3 manifolds | ||
* aspherical threefolds = second and higher homotopy groups vanish | * aspherical threefolds = second and higher homotopy groups vanish | ||
| − | * JSJ decomposition http://en.wikipedia.org/wiki/JSJ_decomposition | + | * JSJ decomposition http://en.wikipedia.org/wiki/JSJ_decomposition |
| − | ** cutting M into | + | ** cutting M into |
*** Seifert fibered pieces ~ non hyperbolic pieces | *** Seifert fibered pieces ~ non hyperbolic pieces | ||
*** atoroidal pieces ~ hyperbolic pieces | *** atoroidal pieces ~ hyperbolic pieces | ||
| − | * Thurston's geometrization | + | * Thurston's geometrization |
** S^3, E\times S^2, Sol | ** S^3, E\times S^2, Sol | ||
** E^3, E\times H^2, SL_2 | ** E^3, E\times H^2, SL_2 | ||
** H^3, Nil | ** H^3, Nil | ||
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==Volume of knot complement== | ==Volume of knot complement== | ||
| + | * Dedekind zeta funciton evaluated at 2 gives a number related to volume of 3-manifold | ||
| + | * {{수학노트|url=블로흐-비그너_다이로그(Bloch-Wigner_dilogarithm)}} | ||
| + | * {{수학노트|url=로바체프스키_함수}} | ||
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==invariants== | ==invariants== | ||
| + | * [[Chern-Simons gauge theory and Witten's invariant]] | ||
| + | * [[Chern-Simons invariant]] | ||
* Turaev-Viro invariant (related to [[6j symbols (Racha coefficient)|6j symbols]]) | * Turaev-Viro invariant (related to [[6j symbols (Racha coefficient)|6j symbols]]) | ||
** Kauffman and Line 'The Temperley Lie algebra recoupling theory and invariants of 3-manifolds" | ** Kauffman and Line 'The Temperley Lie algebra recoupling theory and invariants of 3-manifolds" | ||
** Turaev-Viro "state sum invariants of 3-manifolds and quantum 6j-symbols) | ** Turaev-Viro "state sum invariants of 3-manifolds and quantum 6j-symbols) | ||
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* [[Kashaev's volume conjecture]] | * [[Kashaev's volume conjecture]] | ||
* [[Triangulations and the Bloch group]] | * [[Triangulations and the Bloch group]] | ||
| 53번째 줄: | 39번째 줄: | ||
* [[Number fields and threefolds]] | * [[Number fields and threefolds]] | ||
* [[Reidemeister torsion]] | * [[Reidemeister torsion]] | ||
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==Reshetikihn, Turaev== | ==Reshetikihn, Turaev== | ||
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==history== | ==history== | ||
| 63번째 줄: | 50번째 줄: | ||
* 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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| 75번째 줄: | 62번째 줄: | ||
* [[volume of hyperbolic threefolds and L-values]] | * [[volume of hyperbolic threefolds and L-values]] | ||
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==encyclopedia== | ==encyclopedia== | ||
| − | * http://en.wikipedia.org/wiki/Quantum_invariant | + | * http://en.wikipedia.org/wiki/Quantum_invariant |
| − | * | + | * http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics) |
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==books== | ==books== | ||
| − | * http://www.worldscibooks.com/mathematics/4746.html | + | * Tomotada Ohtsuki [http://www.worldscibooks.com/mathematics/4746.html Quantum Invariants] |
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==expositions== | ==expositions== | ||
| − | * Arithmetic properties of quantum invariants of manifolds http://www.mathnet.ru/php/presentation.phtml?presentid=3937&option_lang=rus Don Zagier | + | * Arithmetic properties of quantum invariants of manifolds http://www.mathnet.ru/php/presentation.phtml?presentid=3937&option_lang=rus Don Zagier |
| − | * Christian Blanchet, Vladimir Turaev [http://www.math.jussieu.fr/%7Eblanchet/Articles/EMP_quantum_inv.pdf Quantum Invariants of 3-manifolds] | + | * Christian Blanchet, Vladimir Turaev [http://www.math.jussieu.fr/%7Eblanchet/Articles/EMP_quantum_inv.pdf Quantum Invariants of 3-manifolds] |
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==articles== | ==articles== | ||
| 115번째 줄: | 94번째 줄: | ||
* Kohno, Toshitake, and Toshie Takata. "Level-Rank Duality of Witten's 3-Manifold Invariants." Progress in algebraic combinatorics 24 (1996): 243. http://tqft.net/other-papers/knot-theory/Level-rank%20duality%20-%20Kohno,%20Takata.pdf | * Kohno, Toshitake, and Toshie Takata. "Level-Rank Duality of Witten's 3-Manifold Invariants." Progress in algebraic combinatorics 24 (1996): 243. http://tqft.net/other-papers/knot-theory/Level-rank%20duality%20-%20Kohno,%20Takata.pdf | ||
* Three-manifolds and the Temperley-Lieb algebra W. B. R. Lickorish, 1991 | * Three-manifolds and the Temperley-Lieb algebra W. B. R. Lickorish, 1991 | ||
| − | * [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions] Don Zagier, | + | * [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions] Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월 |
[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 5월 20일 (월) 06:03 판
fundamental results on three manifolds
- Mostow-Prasad rigidity
- geometrization
maps between threefolds
- maps between aspherical 3 manifolds
- aspherical threefolds = second and higher homotopy groups vanish
- JSJ decomposition http://en.wikipedia.org/wiki/JSJ_decomposition
- cutting M into
- Seifert fibered pieces ~ non hyperbolic pieces
- atoroidal pieces ~ hyperbolic pieces
- cutting M into
- Thurston's geometrization
- S^3, E\times S^2, Sol
- E^3, E\times H^2, SL_2
- H^3, Nil
Volume of knot complement
invariants
- Chern-Simons gauge theory and Witten's invariant
- Chern-Simons invariant
- Turaev-Viro invariant (related to 6j symbols)
- Kauffman and Line 'The Temperley Lie algebra recoupling theory and invariants of 3-manifolds"
- Turaev-Viro "state sum invariants of 3-manifolds and quantum 6j-symbols)
- Kashaev's volume conjecture
- Triangulations and the Bloch group
- Volume of hyperbolic threefolds and L-values and volume of knot complements
- Number fields and threefolds
- Reidemeister torsion
Reshetikihn, Turaev
history
- Topological quantum field theory(TQFT)
- quantum dilogarithm
- Chern-Simons invariant
- Gieseking's constant
- mathematics of x^3-x+1=0
- triangulations and Bloch group
- volume of hyperbolic threefolds and L-values
encyclopedia
- http://en.wikipedia.org/wiki/Quantum_invariant
- http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)
books
- Tomotada Ohtsuki Quantum Invariants
expositions
- Arithmetic properties of quantum invariants of manifolds http://www.mathnet.ru/php/presentation.phtml?presentid=3937&option_lang=rus Don Zagier
- Christian Blanchet, Vladimir Turaev Quantum Invariants of 3-manifolds
articles
- Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links J.M. Borwein, D.J. Broadhurst, 1998
- Gliozzi, F., and R. Tateo. 1995. Thermodynamic Bethe Ansatz and Threefold Triangulations. hep-th/9505102 (May 17). doi:doi:10.1142/S0217751X96001905. http://arxiv.org/abs/hep-th/9505102.
- Kohno, Toshitake, and Toshie Takata. "Level-Rank Duality of Witten's 3-Manifold Invariants." Progress in algebraic combinatorics 24 (1996): 243. http://tqft.net/other-papers/knot-theory/Level-rank%20duality%20-%20Kohno,%20Takata.pdf
- Three-manifolds and the Temperley-Lieb algebra W. B. R. Lickorish, 1991
- Hyperbolic manifolds and special values of Dedekind zeta-functions Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월