6 in chapter 2 ) chapter 3 modular category this chapter consists of four sections . the most contents of the first three sections are taken from [ 23 ] . the section 4 is devote to a similar invariant of 3manifolds given by the author 第三章modular范畴这一章由四节组成，前三节的绝大部分内容取自v . g . turaev的著作[ 23 ] ，第四章介绍了作者得到的一个类似的3维流形不变量，主要结果：定理4
