Exceptional Dehn surgeries on hyperbolic knots and their arrangement

对于三维球面上的双曲纽结，产生非双曲三维流形的Dehn手术称为例外Dehn手术。基本上有三种特殊的Dehn手术。在这个项目中，我们重点研究了晶状体空间手术和环状外科手术，并取得了各种结果。特别地，我给出了对应于三个连续整数的环状手术的双曲纽结的无限族，以及允许环状手术之间的透镜空间手术的双曲纽结的无限族。

For a hyperbolic knot in the 3-sphere, Dehn surgery yielding a non-hyperbolic 3-manifold is called an exceptional Dehn surgery. There are essentially three types of exceptional Dehn surgery. In this project, we focused on lens space surgery and toroidal surgery, and obtained various results. In particular, I gave an infinite family of hyperbolic knots admitting toroidal surgeries corresponding to three consecutive integers, and an infinite family of hyperbolic knots admitting lens space surgery between toroidal surgeries.