| 徐妍,雷逢春,李风玲,梁良.有亏格为1的Heegaard分解的三维流形中的环面纽结[J].数学年刊A辑,2024,(1):1~14 |
| 有亏格为1的Heegaard分解的三维流形中的环面纽结 |
| On Torus Knots in 3-Manifolds with Genus One Heegaard Splitting |
| 投稿时间：2023-07-06 修订日期：2023-12-21 |
| DOI：10.16205/j.cnki.cama.2024.0001 |
| 中文关键词: H’-分解 透镜空间 环面纽结 Seifert流形 |
| 英文关键词:H′-Splitting Lens space Torus knot Seifert manifold |
| 基金项目:国家自然科学基金(No.12071051) |
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| 中文摘要: |
| 将存在亏格为1的Heegaard分解T’1∪F T’2的三维流形记为M=L(p,q),其中p和q是互素整数,q/p为T’2的纬线在T’1上的斜率.若环面F上的简单闭曲线γ在M中非平凡,则称γ是M中的环面纽结.本文对在M中沿环面纽结作m/n-Dehn手术所得流形进行了分类,并给出了两个实心环体沿边界上平环作融合所得流形是L(p,q)中环面纽结补的特征描述. |
| 英文摘要: |
| Let $M=\mathcal{L}(p,q)$ be a 3-manifold which admits a Heegaard splitting $T_1'\cup_F T_2'$ of
genus 1, where $p$ and $q$ are co-prime integers, and a meridian curve of $T_2'$ has the slope $s=q/p$ on $T_1'$.
A simple closed curve $\gamma$ on the torus $F$ is called a torus knot in $M$ if it is non-trivial
in $M$. The main results of the paper are as follows: the authors classify the manifolds obtained by performing
a $m/n$-Dehn surgery along a torus knot in $M$, and describe the characteristics for the manifold
obtained by gluing two solid tori together along an annulus on the boundary of each solid torus
to be a torus knot complement in $\mathcal{L}(p,q)$. |
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