A Lower Bound for the Heegaard Genera of Annulus Sum

作     者：Feng Ling LI Feng Chun LEI 

作者机构：School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2011年第31卷第4期

页      面：578-586页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Fundamental Research Funds for the Central Universities and the Key Grant of National NaturalScience Foundation of China (Grant No.10931005) 

主　　题：genus distance annulus. 

摘      要：Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2