"3-manifolds and their invariants"의 두 판 사이의 차이
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* 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 $3$-manifolds.” The Bulletin of the London Mathematical Society 15 (5): 401–487. doi:10.1112/blms/15.5.401. | ||
2013년 11월 5일 (화) 09:42 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
- 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
- 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
- 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