三维流形不变量的等价表示

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.

The Equivalent Representations of Invariants for 3-Ma

Let Mbe a 3-manifold obtained by surgery on then-component framed link L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 representations 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.}