"3-manifolds and their invariants"의 두 판 사이의 차이

2015년 10월 3일 (토) 15:32 판

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
Thurston's geometrization
- S^3, E\times S^2, Sol
- E^3, E\times H^2, SL_2
- H^3, Nil

Dedekind zeta funciton evaluated at 2 gives a number related to volume of 3-manifold
틀:수학노트
틀:수학노트

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

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.

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

@@ 86번째 줄: / 86번째 줄: @@
 ==articles==
+* 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