"3-manifolds and their invariants"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 64번째 줄: | 64번째 줄: | ||
* [http://www.geometrygames.org/SnapPea/ snappea] | * [http://www.geometrygames.org/SnapPea/ snappea] | ||
* [http://sourceforge.net/projects/snap-pari/ snap] | * [http://sourceforge.net/projects/snap-pari/ snap] | ||
| + | * [http://regina.sourceforge.net/ Regina] | ||
* [http://www.math.utk.edu/%7Emorwen/knotscape.html http://www.math.utk.edu/~morwen/knotscape.html] | * [http://www.math.utk.edu/%7Emorwen/knotscape.html http://www.math.utk.edu/~morwen/knotscape.html] | ||
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* http://en.wikipedia.org/wiki/Quantum_invariant<br> | * http://en.wikipedia.org/wiki/Quantum_invariant<br> | ||
* http://ko.wikipedia.org/wiki/[http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 ] | * http://ko.wikipedia.org/wiki/[http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 ] | ||
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* http://www.worldscibooks.com/mathematics/4746.html<br> | * http://www.worldscibooks.com/mathematics/4746.html<br> | ||
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* [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<br> | * [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<br> | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 5월 18일 (토) 07:05 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
- KnotData[]
KnotData["FigureEight", "HyperbolicVolume"]
N[%, 20]
- Dedekind zeta funciton evaluated at 2 gives a number related to volume of 3-manifold
- Bloch-Wigner dilogarithm is involved
a problem
- Prove
$$ \begin{align} \frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt & =\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7})) \\ & = \frac{2}{\sqrt{7}}(Cl(2\pi /7)+Cl(4\pi/7)-Cl(6\pi/7)) \end{align} $$ - a log tangent integral
invariants
- 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)
- Chern-Simons invariant
- 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
software
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
books
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.
- 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