Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2017-11-01

Journal: CHINESE ANNALS OF MATHEMATICS SERIES B

Included Journals: SCIE

Volume: 38

Issue: 6

Page Number: 1373-1380

ISSN: 0252-9599

Key Words: Complete surface system; Complete spanning curve system; Heegaard diagram; Handlebody addition

Abstract: 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.