论文标题
装有必需的两次托里的结歧管的dehn填充物
Dehn fillings of knot manifolds containing essential twice-punctured tori
论文作者
论文摘要
我们表明，如果双曲线歧管$ m $包含带边界斜率$β$的两次圆环$ f $，并承认带有斜坡$α$的填充物，产生塞弗特纤维纤维空间，那么坡度$α$和$β$之间的距离是$ 5 $或等于$ 5 $ $ $ $ m $ n n exter of the Exter of the 8 Knkot of Exter of the 8 Knkot。结果是锋利的； $ 5 $的界限可以在无限的许多双曲结歧管上实现。在$α$填充的基本组中，我们还确定了距离界限。证明分为四种情况$ f $是半纤维，$ f $是光纤，$ f $是不分开的，但不是光纤，而$ f $是分离的，但不是半纤维，我们在每种情况下都获得了精致的界限。
We show that if a hyperbolic knot manifold $M$ contains an essential twice-punctured torus $F$ with boundary slope $β$ and admits a filling with slope $α$ producing a Seifert fibred space, then the distance between the slopes $α$ and $β$ is less than or equal to $5$ unless $M$ is the exterior of the figure eight knot. The result is sharp; the bound of $5$ can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the $α$-filling contains no non-abelian free group. The proofs are divided into the four cases $F$ is a semi-fibre, $F$ is a fibre, $F$ is non-separating but not a fibre, and $F$ is separating but not a semi-fibre, and we obtain refined bounds in each case.
