三维流形不变量的等价表示  

The Equivalent Representations of Invariants for 3-Ma

作　　者：韩友发[1] 张倩[1] 樊星[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林大学学报（理学版）》2009年第2期179-184,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10771023);辽宁省教育厅资助项目基金(批准号:05L208)

摘　　要：设M是由S3中通过标架环链(L,f)做手术得到的三维流形,对于标架环链(L,f)可以得到保持同痕及K+和K-变换的环链不变量,进而得到三维流形M的不变量,从而三维流形不变量可以由L的Kauffman括号的有限线性组合给出,当取变量为第4r个复单位根时,利用括号多项式、Temperly-Lieb代数、Jones-Kauffman模、线性束理论等给出了不同的三维流形不变量的表示.证明了这些三维流形不变量的表示是等价的,同时给出了三维流形不变量的一个新表示.Let M be a 3-manifold obtained by surgery on the n-component framed link L belong to S^3. We can get the link invariant maintaining isotopy, and K＋ and K- moves for the framed link （L, f）, so as to furthermore obtain the invariant for 3-manifold. Thus the invariants for 3-manifold are given by finite linear combinations of Kauffman brackets of cabling of L, to be evaluated at primitive 4r-th root of unity. Some difference representa- tions of invariant for 3-manifold are given by using the bracket polynomial, Temperly-Lieb algebra, Jones- Kauffman module and linear skein theory, etc. This paper deals with the relation of these representations of invariants, and shows essentially the consistency of them. A new representation of the invariant of 3-manifolds is also given.

关 键 词：标架环链 不变量表示 括号多项式 Jones—Kauffman模 

分 类 号：O189.3[理学—数学]