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

수학노트

둘러보기로 가기 검색하러 가기

2012년 10월 28일 (일) 17:04 판

introduction==
volume of knot complements

Chern-Simons invariant of manifolds

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)

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

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
\(\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=\frac{2}{\sqrt{7}}(Cl(2\pi /7})+Cl(4\pi/7})-Cl(6\pi/7}))\)

a log tangent integral

Reshetikihn, Turaev==
software

snappea

snap

http://www.math.utk.edu/~morwen/knotscape.html

history==
http://www.google.com/search?hl=en&tbs=tl:1&q=

하위페이지

threefolds and their invariants

Chern-Simons invariant

Gieseking's constant

mathematics of x^3-x+1=0

triangulations and Bloch group

volume of hyperbolic threefolds and L-values

related items4667393==
quantum dilogarithm

encyclopedia==
http://en.wikipedia.org/wiki/Quantum_invariant

http://ko.wikipedia.org/wiki/[1]

http://en.wikipedia.org/wiki/

Princeton companion to mathematics(Companion_to_Mathematics.pdf)

books==
http://www.worldscibooks.com/mathematics/4746.html

2010년 books and articles
4909919
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

http://dx.doi.org/10.1063/1.3085764

question and answers(Math Overflow)==
http://mathoverflow.net/search?q=

http://mathoverflow.net/search?q=

blogs==
구글 블로그 검색

http://blogsearch.google.com/blogsearch?q=

http://blogsearch.google.com/blogsearch?q=

experts on the field==
http://arxiv.org/

links==
Detexify2 - LaTeX symbol classifier

수식표현 안내

The On-Line Encyclopedia of Integer Sequences

원본 주소 "https://wiki.mathnt.net/index.php?title=3-manifolds_and_their_invariants&oldid=43568"

개인노트