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} ...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, ?S = {?S_1, ···, ?S_n}is a complete curve system on F. We call S a complete surface system for M, and ?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 ?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 Hn.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11329101,11431009,11329101,11471151,11401069)the grant of the Fundamental Research Funds for the Central Universities(No.DUT14LK12)
文摘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, ?S = {?S_1, ···, ?S_n}is a complete curve system on F. We call S a complete surface system for M, and ?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 ?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 Hn.
