N股Montesinos纽结的着色Jones多项式
The Colored Jones Polynomial of N-String Montesinos Knots
摘要: 本文运用纽结三价图计算了当n≥4时，n股Montesinos纽结的着色Jones多项式。算法的关键是构造从θ图到n股Montesinos纽结的三价图变换过程，该算法与n=3的情况有着本质不同。
Abstract:
In this paper we calculate the colored Jones polynomial of n-string Montesinos knots for n≥4 us-ing knotted trivalent graphs. The key point of the algorithm is to construct the operations from a θ graph to a Montesinos knot, and the algorithm has essential difference with the case n=3 .
参考文献
|
[1]
|
Jones, V.F. (1985) A Polynomial Invariant for Knots via Von Neumann Algebras. Bulletin of the American Mathemati-cal Society, 12, 103-111. [Google Scholar] [CrossRef]
|
|
[2]
|
Witten, E. (1989) Quantumfield Theory and the Jones Polynomial. Communications in Mathematical Physics, 121, 351-399. [Google Scholar] [CrossRef]
|
|
[3]
|
Reshetikhin, N. and Turaev, V.G. (1991) Invariants of 3-Manifolds via Link Polynomials and Quantum Groups. Inventiones Mathematicae, 103, 547-597. [Google Scholar] [CrossRef]
|
|
[4]
|
Lee, C.R.S. and van der Veen, R. (2016) Slopes for Pretzel Knots. The New York Journal of Mathematics, 22, 1339-1364.
|
|
[5]
|
Leng, X., Yang, Z. and Liu, X. (2019) The Slope Conjectures for 3-String Montesinos Knots. The New York Journal of Mathematics, 25, 45-70.
|
|
[6]
|
Thurston, D.P. (2002) The Al-gebra of Knotted Trivalent Graphs and Turaev’s Shadow World. Geometry & Topology Monographs, 4, 337-362.
|
|
[7]
|
Garoufalidis, S., Lee, C.R.S. and Roland, V.D.V. (2018) The Slope Conjecture for Montesinos Knots. arXiv.1807.00957.
|