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

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.

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.