"3-manifolds and their invariants"의 두 판 사이의 차이
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| − | == | + | ==fundamental results on three manifolds== |
| + | * Mostow-Prasad rigidity | ||
| + | * geometrization | ||
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==maps between threefolds== | ==maps between threefolds== | ||
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* 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== |
| − | + | * [[Chern-Simons gauge theory and Witten's invariant]] | |
| − | + | * [[Chern-Simons invariant]] | |
| − | + | * 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" | |
| − | + | ** Turaev-Viro "state sum invariants of 3-manifolds and quantum 6j-symbols) | |
| − | + | * [[Kashaev's volume conjecture]] | |
| − | + | * [[Ideal triangulations of 3-manifolds and the Bloch invariant]] | |
| − | * | + | * [[Volume of hyperbolic threefolds and L-values]] and volume of knot complements |
| − | * [[ | + | * [[Number fields and threefolds]] |
| + | * [[Reidemeister torsion]] | ||
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==Reshetikihn, Turaev== | ==Reshetikihn, Turaev== | ||
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==history== | ==history== | ||
| 68번째 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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| − | ==== | + | ==related items== |
| + | * [[Topological quantum field theory(TQFT)]] | ||
| + | * [[quantum dilogarithm]] | ||
| + | * [[Chern-Simons gauge theory and invariant|Chern-Simons invariant]] | ||
| + | * [[Gieseking's constant]] | ||
| + | * [[mathematics of x^3-x+1=0]] | ||
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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== | ||
| + | * Saveliev, Nikolai. 1999. Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant. Walter De Gruyter Inc. http://www.amazon.com/Lectures-Topology-3-Manifolds-Introduction-Invariant/dp/3110162725 | ||
| + | * Tomotada Ohtsuki [http://www.worldscibooks.com/mathematics/4746.html Quantum Invariants] | ||
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==expositions== | ==expositions== | ||
| − | + | * Delp, Kelly, Diane Hoffoss, and Jason Fox Manning. “Problems In Groups, Geometry, and Three-Manifolds.” arXiv:1512.04620 [math], December 14, 2015. http://arxiv.org/abs/1512.04620. | |
| − | * 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] |
| − | + | * Scott, Peter. 1983. “The Geometries of <math>3</math>-manifolds.” The Bulletin of the London Mathematical Society 15 (5): 401–487. doi:10.1112/blms/15.5.401. | |
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==articles== | ==articles== | ||
| − | + | * Maria, Clément, and Jonathan Spreer. “Admissible Colourings of 3-Manifold Triangulations for Turaev-Viro Type Invariants.” arXiv:1512.04648 [cs, Math], December 14, 2015. http://arxiv.org/abs/1512.04648. | |
| + | * Friedl, Stefan, and Wolfgang Lück. “The L^2-Torsion Function and the Thurston Norm of 3-Manifolds.” arXiv:1510.00264 [math], October 1, 2015. http://arxiv.org/abs/1510.00264. | ||
| + | * Kuperberg, Greg. “Algorithmic Homeomorphism of 3-Manifolds as a Corollary of Geometrization.” arXiv:1508.06720 [math], August 27, 2015. http://arxiv.org/abs/1508.06720. | ||
* [http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links] J.M. Borwein, D.J. Broadhurst, 1998 | * [http://arxiv.org/abs/hep-th/9811173 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:[http://dx.doi.org/10.1142/S0217751X96001905 10.1142/S0217751X96001905]. http://arxiv.org/abs/hep-th/9505102. | * 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. | ||
| + | * 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 |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
| + | [[분류:TQFT]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q526901 Q526901] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LEMMA': '3-manifold'}] | ||
2021년 2월 17일 (수) 01:12 기준 최신판
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
- Ideal triangulations of 3-manifolds and the Bloch invariant
- 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
encyclopedia
- http://en.wikipedia.org/wiki/Quantum_invariant
- http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)
books
- Saveliev, Nikolai. 1999. Lectures on the Topology of 3-Manifolds: An Introduction to the Casson Invariant. Walter De Gruyter Inc. http://www.amazon.com/Lectures-Topology-3-Manifolds-Introduction-Invariant/dp/3110162725
- Tomotada Ohtsuki Quantum Invariants
expositions
- Delp, Kelly, Diane Hoffoss, and Jason Fox Manning. “Problems In Groups, Geometry, and Three-Manifolds.” arXiv:1512.04620 [math], December 14, 2015. http://arxiv.org/abs/1512.04620.
- 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
- Scott, Peter. 1983. “The Geometries of \(3\)-manifolds.” The Bulletin of the London Mathematical Society 15 (5): 401–487. doi:10.1112/blms/15.5.401.
articles
- Maria, Clément, and Jonathan Spreer. “Admissible Colourings of 3-Manifold Triangulations for Turaev-Viro Type Invariants.” arXiv:1512.04648 [cs, Math], December 14, 2015. http://arxiv.org/abs/1512.04648.
- Friedl, Stefan, and Wolfgang Lück. “The L^2-Torsion Function and the Thurston Norm of 3-Manifolds.” arXiv:1510.00264 [math], October 1, 2015. http://arxiv.org/abs/1510.00264.
- Kuperberg, Greg. “Algorithmic Homeomorphism of 3-Manifolds as a Corollary of Geometrization.” arXiv:1508.06720 [math], August 27, 2015. http://arxiv.org/abs/1508.06720.
- 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
메타데이터
위키데이터
- ID : Q526901
Spacy 패턴 목록
- [{'LEMMA': '3-manifold'}]