Representations of Knot Groups and Twisted Alexander Polynomials
Representations of Knot Groups and Twisted Alexander Polynomials
摘要
We present a twisted version of the Alexander polynomial associated with a matrix rep- resentation of the knot group.Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.
We present a twisted version of the Alexander polynomial associated with a matrix rep- resentation of the knot group.Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.
参考文献10
-
1Freyd P,Yetter D,Hoste J,Lickorish WBR,Millett K,Ocneanu A.A new polynomial invariant of knots and links[].Bulletin of the American Mathematical Society.1985
-
2Wada,M.Twisted Alexander polynomial for finitely presented groups[].Topology.1994
-
3T. Kitano.Twisted Alexander polynomial and Reidemeister torsion[].Pacific Journal of Mathematics.1996
-
4Kirk,P.,Livingston,C.Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants[].Topology.1999
-
5P. Kirk,C. Livingston.Twisted knot polynomials: inversion, mutation and concordance[].Topology.1999
-
6Reidemeister,K. Knotentheorie . 1948
-
7Rolfsen,D. Knots and Links. Math . 1976
-
8S.Cappell,R.Lee,E.Miller.A symplectic geometry approach to generalized Casson’’s invariants of 3manifold[].BullAMS.1990
-
9B.Jiang,S Wang.Twisted topological invariants associated with representations[].Topics ia knot theory.1993
-
10R.H.Fox.A quick trip through knot theory[].Topology of manifolds.1960
-
1Zou Liping,Zhang Pengming,D.G.Pak.1 - 25 Knot Topology in QCD[J].IMP & HIRFL Annual Report,2013(1):30-30.
-
2刘永恺,杨师杰.Three-dimensional solitons in two-component Bose–Einstein condensates[J].Chinese Physics B,2014,23(11):198-201.
-
3You Fa HAN Xiao Sha MA.Knots and Polynomials[J].Journal of Mathematical Research and Exposition,2010,30(2):257-264. 被引量:1
-
4Weiping LiDepartment of Mathematics,Oklahoma State University,Stillwater,Oklahoma 74078-0613,USA.The Symplectic Floer Homology of the Square Knot and Granny Knots[J].Acta Mathematica Sinica,English Series,1999,15(1):1-10.
-
5邵常贵,潘贵军,邵亮,陈中秋,肖俊华.真空哈密顿约束对扩展knot态的作用计算[J].物理学报,2000,49(4):619-625. 被引量:2
-
6LIN Fanghua & YANG YisongCourant Institute of Mathematical Sciences, New York University, New York, New York 10012, U. S. A.School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U. S. A.,Department of Mathematics, Polytechnic University, Brooklyn, New York 11201, U. S. A..The Faddeev knots as stable solitons: Existence theorems[J].Science China Mathematics,2004,47(2):187-197. 被引量:11
-
7Zou Liping,Zhang Pengming,D.G. Pak.1 - 26 Exact Knot Solutions in a Generalized Skyrme-Faddeev Model[J].IMP & HIRFL Annual Report,2013(1):31-31.
-
8任继荣,墨淑凡,朱涛.Knot solitons in the AFZ model[J].Chinese Physics B,2009,18(5):1814-1820.
-
9Ye XIAO,Zaixing HUANG.Geometric effects of cross sections on equilibrium of helical and twisted ribbon[J].Applied Mathematics and Mechanics(English Edition),2017,38(4):495-504. 被引量:1
-
10齐东旭,李华山.Many-knot spline technique for approximation of data[J].Science China(Technological Sciences),1999,42(4):383-387. 被引量:4