Three-dimensional Manifold Invariant Representation

This papermainly studies the represent ion of invariants for 3-manifold. Let 3-manifold M be obtained by surgery on the n?ccnpone framed link L?S~3. We can get the link invariant which are unchanged under (regular)isotopy K_+ and K__ moves, for the framed link(L,f) , furthermore, obtain the invariant for 3-manifold Thus, the invariants for 3-manifold are given by finite linear ccmbinations of Kauffman brackets of cabling of L, to be evaluated at primitive 4r h root of unity. Some different representions of invariant for 3-manifold are given by using the bracket polynomial Temperly Lieb algebra Jones Kauffman module and linear skein theory, etc On the one hand, this paper discusses the relation of these representions of invariants and shows essentially the consistency of than On the other hand let B denote the Jones Kauffman module of the solid torus the same.