论文标题
扭曲结中的完全测量表面补充
Totally geodesic surfaces in twist knot complements
论文作者
论文摘要
在本文中，我们给出明确的例子，说明了许多不可遵循的（非占用）双曲线$ 3 $ -Manifolds完全承认$ k $完全是Geodesic $ k $，以回答Bader，Fisher，Miller和Stover的问题。该结构来自一个扭曲的家族及其二面盖。 $ k = 1 $的案例来自沉浸式的完全大地测量三次的球体的独特性，回答了里德的问题。我们采用主要结果的证明技术，明确构建了无限的covolume在扭结组中的非质量最大紫红色亚组，我们还表明，没有曲折的结与奇怪的prime半扭曲的补充是在Champanerkar，Kofman，Kofman和Purcell的意义上，是正确的。
In this article, we give explicit examples of infinitely many non-commensurable (non-arithmetic) hyperbolic $3$-manifolds admitting exactly $k$ totally geodesic surfaces for any positive integer $k$, answering a question of Bader, Fisher, Miller and Stover. The construction comes from a family of twist knot complements and their dihedral covers. The case $k=1$ arises from the uniqueness of an immersed totally geodesic thrice-punctured sphere, answering a question of Reid. Applying the proof techniques of the main result, we explicitly construct non-elementary maximal Fuchsian subgroups of infinite covolume within twist knot groups, and we also show that no twist knot complement with odd prime half twists is right-angled in the sense of Champanerkar, Kofman, and Purcell.
