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

2013년 6월 2일 (일) 07:11 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

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

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

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

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 ==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]