论文标题
双曲结理论
Hyperbolic Knot Theory
论文作者
论文摘要
这本书是第三维中双曲几何形状的介绍，及其在结理论和结理论中产生的几何问题上的应用。它有三个部分。第一部分涵盖了3个manifolds上双曲线几何和几何结构的基本工具。第二部分的重点是可以通过双曲线几何形状，尤其是扭结，2桥结和交替结研究的结和链接系列。它还开发了用于研究这些家族的几何技术，例如角结构和正常表面。第三部分给出了直接来自双曲线几何形状，即体积，规范多面体和A-Polynomial的三个重要结的详细信息。
This book is an introduction to hyperbolic geometry in dimension three, and its applications to knot theory and to geometric problems arising in knot theory. It has three parts. The first part covers basic tools in hyperbolic geometry and geometric structures on 3-manifolds. The second part focuses on families of knots and links that have been amenable to study via hyperbolic geometry, particularly twist knots, 2-bridge knots, and alternating knots. It also develops geometric techniques used to study these families, such as angle structures and normal surfaces. The third part gives more detail on three important knot invariants that come directly from hyperbolic geometry, namely volume, canonical polyhedra, and the A-polynomial.
