张明星.Heegaard splittings 的曲面连通和[J].数学研究及应用,2009,29(3):558~562
Heegaard splittings 的曲面连通和
Surface Sum of Heegaard Splittings
投稿时间:2007-03-16  修订日期:2007-05-26
DOI:10.3770/j.issn:1000-341X.2009.03.022
中文关键词:  Heegaard 分解  可稳定化的  不可稳定化的.
英文关键词:Heegaard splitting  stabilized  amalgamation.
基金项目:博士点新教师基金(No.200801411069).
作者单位
张明星 大连理工大学数学科学学院, 辽宁 大连 116024 
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中文摘要:
      设$M_i=V_i\cup W_i$ ($i=1,2$)是两个Heegaards分解.设$F_i \subset\partial_-W_i$,则$F_1$到$F_2$的同胚映射给出了粘贴流形 $M=M_1\cup_{F_1=F_2}M_2$.在本篇文章中我们定义了新流形的Heegaard分解.并给出了新的Heegaard分解是不可稳定化的一个充分条件.
英文摘要:
      Suppose $M_i=V_i\cup W_i$~($i=1,2$) are Heegaard splittings. A homeomorphism $f:F_1\rightarrow F_2$ produces an attached manifold $M=M_1\cup_{F_1=F_2}M_2$, where $F_i \subset \partial_-W_i$. In this paper we define a surface sum of Heegaard splittings induced from the Heegaard splittings of $M_1$ and $M_2$, and give a sufficient condition when the surface sum of Heegaard splitting is stabilized. We also give examples showing that the surface sum of Heegaard splittings can be unstabilized. This indicates that the surface sum of Heegaard splittings and the amalgamation of Heegaard splittings can give different Heegaard structures.
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