| 李阳,雷逢春.关于内亏格1的弱可约SD-分解(英)[J].数学研究及应用,2006,26(4):694~698 |
| 关于内亏格1的弱可约SD-分解(英) |
| On Weakly Reducible SD-Splittings of Inner Genus 1 |
| 投稿时间：2006-02-15 |
| DOI：10.3770/j.issn:1000-341X.2006.04.007 |
| 中文关键词: SD-分解 可约性 内亏格. |
| 英文关键词:SD-splitting reducibility inner genus |
| 基金项目:国家自然科学基金 (10571034) |
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| 中文摘要: |
| 设$(M; H_{1},H_{2};F_{0})$为带边3-流形$M$的一个SD-分解.称该分解为可约的（或弱可约的）若存在本质圆片$D_1\subset H_1$，$D_2\subset H_2$使得$\partial D_1,\partial D_2\subset F_0$并且$\partial D_1=\partial D_2$ (或$\partial D_1\cap\partial D_2=\emptyset$). 称$(M; H_{1}, H_{2}; F_{0})$为内亏格1若$F_0$为穿孔环面.本文主要结果：一个弱可约的内亏格1的SD-分解或是可约的或是双经的. |
| 英文摘要: |
| Let $(M; H_{1},H_{2};F_{0})$ be a SD-splitting for bordered 3-manifold $M$. The splitting is reducible (weakly reducible, respectively) if there exist essential disks $D_1\subset H_1$ and $D_2\subset H_2$ such that $\partial D_1,\partial D_2\subset F_0$ and $\partial D_1=\partial D_2$ ($\partial D_1\cap\partial D_2=\emptyset$, respectively). A SD-splitting $(M; H_{1},H_{2};F_{0})$ for bordered 3-manifold $M$ is of inner genus 1 if $F_0$ is a punctured torus. In the present paper, we show that a weakly reducible SD-splitting of inner genus 1 is either reducible or bilongitudional. |
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