Exceptional Dehn surgeries on hyperbolic knots and their arrangement

对于三维球面中的双曲纽结，产生非双曲三维流形的Dehn手术称为例外Dehn手术。基本上有三种类型的特殊Dehn手术。在本项目中，我们重点研究了透镜空间手术和环形手术，并获得了各种结果。特别是，我给了一个无限家庭的双曲结承认环形手术对应于三个连续的整数，和一个无限家庭的双曲结承认透镜空间手术之间的环形手术。

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.