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

作　　者：徐妍 雷逢春[1] 李风玲 梁良 XU Yan;LEI Fengchun;LI Fengling;LIANG Liang(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,Liaoning,China;School of Mathematics,Liaoning Normal University,Dalian 116029,Liaoning,China)

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《数学年刊（A辑）》2024年第1期1-14,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12071051)的资助。

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.Let M=L(p,q)be a 3-manifold which admits a Heegaard splitting T'_(1)∪_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 curveγon 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 L(p,q).

关 键 词：H’-分解 透镜空间 环面纽结 Seifert流形 

分 类 号：O189.21[理学—数学]