| 刘贺,雷逢春,李风玲.两个压缩体融合为一个压缩体的充分必要条件*[J].数学年刊A辑,2022,43(4):357~366 |
| 两个压缩体融合为一个压缩体的充分必要条件* |
| A Sufficient and Necessary Condition for a Surface Sum of Two Compression Bodies to be a Compression Body |
| Received:September 29, 2021 Revised:February 27, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0023 |
| 中文关键词: 压缩体, 3维流形融合, Heegaard分解 |
| 英文关键词:Compression body, Amalgamated 3-manifold, Heegaard splitting |
| 基金项目:国家自然科学基金(No.12071051)和中央高校基本科研业务费(No.DUT21LAB302) |
| Author Name | Affiliation | | LIU He | School of Mathematical Sciences, Dalian University of Technology,Dalian 116024, Liaoning, China. | | LEI Fengchun | School of Mathematical Sciences, Dalian University of Technology,Dalian 116024, Liaoning, China. | | LI Fengling | School of Mathematical Sciences, Dalian University of Technology,Dalian 116024, Liaoning, China. |
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| 中文摘要: |
| 本文给出了两个压缩体沿紧致连通曲面(带边曲面或闭曲面)融合仍是一个压缩体(有非空负边界)的充分必要条件,还给出了两个3维流形沿着边界上的紧致连通带边曲面融合中的融合曲面为边界不可压缩的一个特征描述,同时还证明了压缩体的每个Heegaard分解是标准的. |
| 英文摘要: |
| In the paper, the authors give a sufficient and necessary condition for an amalgamation of two compression bodies along a connected surface to be a compression body, and a characteristic for the amalgamated surface to be ?-incompressible in the amalgamation of two 3-manifolds along a compact connected surface with non-empty boundary. They also show that every Heegaard splitting of a compression body is standard. |
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