纽结Jones多项式根的性质
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摘要
研究了链环和纽结的Jones多项式性质和根分布.利用环链的Jones多项式的某些性质和正弦、余弦函数的性质给出:当n≤5时,单位根e2p+1/nπi不是环面结T_(p,q)(其中(p,q)=1)的Jones多项式的零点.
The properties of Jones polynomial of knots and links and their zero points distributions were studied.It concluded that unit roots were not the zeros of the Jones polynomial for torus knots T_(p,q)( while( p,q) =1) by using some properties of the Jones polynomial for knots and the related knowledge of sine and consine function.
The properties of Jones polynomial of knots and links and their zero points distributions were studied.It concluded that unit roots were not the zeros of the Jones polynomial for torus knots T_(p,q)( while( p,q) =1) by using some properties of the Jones polynomial for knots and the related knowledge of sine and consine function.
引文
[1]ALEXANDER J W.Topological invariants of knots and links[J].Trans Amer Math Soci,1928,30(2):275-306.
[2]KAUFFMAN L H.State models and the Jones polynomial[J].Topology,1987,26:395-407.
[3]KAUFFMAN L H.New invariants in the theory knots[J].Amer Math Monthly,1988,953:195-242.
[4]JONES V F R.A polynomial invariant for knots via von Neumann algebras[J].Bull Am Math Soc,1985,12:103-111.
[5]WU F,WANG J.Zeros of Jones polynomials[J].Physica A,2001,296:483-494.
[6]CHANG S C,SHROCK R.Zeros of the Jones polynomials for families of knots and links[J].Physica A,2001,301:196-218.
[7]JIN X A,ZHANG F J.Zeros of the Jones polynomial are dense in the complex plane[J].Elec J Comb,2010,17(1):2493-2503.
[8]陶志雄.Jones多项式的零点[J].数学年刊,2011,32A(1):63-70.
[9]HAN Y F,ZHANG R W.Zeros of the Jones Polynomial for torus knots and 2-bridge knots[J].Chin Quart J Math,2014(4):612-629.
[2]KAUFFMAN L H.State models and the Jones polynomial[J].Topology,1987,26:395-407.
[3]KAUFFMAN L H.New invariants in the theory knots[J].Amer Math Monthly,1988,953:195-242.
[4]JONES V F R.A polynomial invariant for knots via von Neumann algebras[J].Bull Am Math Soc,1985,12:103-111.
[5]WU F,WANG J.Zeros of Jones polynomials[J].Physica A,2001,296:483-494.
[6]CHANG S C,SHROCK R.Zeros of the Jones polynomials for families of knots and links[J].Physica A,2001,301:196-218.
[7]JIN X A,ZHANG F J.Zeros of the Jones polynomial are dense in the complex plane[J].Elec J Comb,2010,17(1):2493-2503.
[8]陶志雄.Jones多项式的零点[J].数学年刊,2011,32A(1):63-70.
[9]HAN Y F,ZHANG R W.Zeros of the Jones Polynomial for torus knots and 2-bridge knots[J].Chin Quart J Math,2014(4):612-629.