点击次数：

论文类型：期刊论文

发表时间：2017-11-01

发表刊物：CHINESE ANNALS OF MATHEMATICS SERIES B

收录刊物：SCIE

卷号：38

期号：6

页面范围：1373-1380

ISSN号：0252-9599

关键字：Complete surface system; Complete spanning curve system; Heegaard diagram; Handlebody addition

摘要：Let M be a compact connected 3-submanifold of the 3-sphere S-3 with one boundary component F such that there exists a collection of n pairwise disjoint connected orientable surfaces S = {S-1, ... , S-n} properly embedded in M, partial derivative S = {partial derivative S-1, ... , partial derivative S-n} is a complete curve system on F. We call S a complete surface system for M, and partial derivative S a complete spanning curve system for M. In the present paper, the authors show that the equivalent classes of complete spanning curve systems for M are unique, that is, any complete spanning curve system for M is equivalent to partial derivative S. As an application of the result, it is shown that the image of the natural homomorphism from the mapping class group M (M) to M (F) is a subgroup of the handlebody subgroup H-n.