论文标题
双曲线结的特殊手术
Exceptional surgeries on hyperbolic fibered knots
论文作者
论文摘要
令$ k \ subset S^3 $为双曲线纤维结，使$ s^3_ {p/q}（k）$，$ \ frac pq $ - $ k $的手术，是非hyperbolic。我们证明，如果$ k $的单片是正确的，则$ 0 \ le \ frac pq \ le 4g（k）$。如果$ s^3_ {p/q}（k）$是一个小的Seifert Fimert L-Space，则无法获得上限$ 4G（k）$。如果$ k $的单片既不是右手，也不是左手，则$ | q | \ le3 $。 作为推论，对于任何给定的正圆环$ t $，如果$ p/q \ ge4g（t）+4 $，则$ p/q $是斜坡的特征。这改善了Ni-Zhang和McCoy的早期范围。我们还证明了某些有限/环状斜率正在表征。更确切地说，$ 14 $的特征是$ t_ {4,3} $，$ 17 $的特征是$ t_ {5,3} $，而$ 4N+1 $的特征是$ t_ {2n+1,2} $，除$ n = 5 $时。到了最近的tange定理，这表明$ t_ {2n+1,2} $是$ s^3 $中唯一的结，而亚历山大多项式则具有$ t^n-t^{n-t^{n-1}+t^{n-1}+t^{n-2}+t^{n-2}+\ text+text {sister forts {sister forts {sistor corter} $。 在附录中，我们证明，如果纤维结的结式浮子同源性的第二个等级为$ 1 $，那么单曲子是右弯曲或左弯曲的。
Let $K\subset S^3$ be a hyperbolic fibered knot such that $S^3_{p/q}(K)$, the $\frac pq$--surgery on $K$, is non-hyperbolic. We prove that if the monodromy of $K$ is right-veering, then $0\le\frac pq\le 4g(K)$. The upper bound $4g(K)$ cannot be attained if $S^3_{p/q}(K)$ is a small Seifert fibered L-space. If the monodromy of $K$ is neither right-veering nor left-veering, then $|q|\le3$. As a corollary, for any given positive torus knot $T$, if $p/q\ge4g(T)+4$, then $p/q$ is a characterizing slope. This improves earlier bounds of Ni--Zhang and McCoy. We also prove that some finite/cyclic slopes are characterizing. More precisely, $14$ is characterizing for $T_{4,3}$, $17$ is characterizing for $T_{5,3}$, and $4n+1$ is characterizing for $T_{2n+1,2}$ except when $n=5$. By a recent theorem of Tange, this shows that $T_{2n+1,2}$ is the only knot in $S^3$ admitting a lens space surgery while the Alexander polynomial has the form $t^n-t^{n-1}+t^{n-2}+\text{lower order terms}$. In the appendix, we prove that if the rank of the second term of the knot Floer homology of a fibered knot is $1$, then the monodromy is either right-veering or left-veering.
