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| On Torus Knots in 3-Manifolds with Genus One Heegaard Splitting |
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Citation： |
徐妍,雷逢春,李风玲,梁良.On Torus Knots in 3-Manifolds with Genus One Heegaard Splitting[J].Chinese Annals of Mathematics B,2024,45(1):1~14 |
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Net amount： 143 |
Authors： |
徐妍; 雷逢春;李风玲;梁良 |
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| Abstract： |
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 $\mathcal{L}(p,q)$. |
Keywords： |
H′-Splitting Lens space Torus knot Seifert manifold |
Classification： |
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