论文标题
dehn手术和双曲结，没有隐藏对称性的补充
Dehn surgery and hyperbolic knot complements without hidden symmetries
论文作者
论文摘要
诺伊曼（Neumann）和里德（Reid）猜想，正好有三个结的补充，可以接收隐藏的对称性。本文建立了一些结果，可以证明猜想。我们的主要技术工具提供了障碍物，可以使许多刺穿的歧管生产结的填充物补充，以承认隐藏的对称性。应用这些工具，我们显示了任何两桥链接补充的补充，最多有限的一个尖齿填充物可以被结的补充所覆盖，以承认隐藏的对称性。我们还表明，八八音的补充是唯一的结，体积小于$ 6V_0 \约6.0896496 $，允许隐藏的对称性。然后，我们以两个独立的证据结论，在双曲结中，只有图形结的补充可以接收隐藏的对称性，并覆盖了两桥链接补充$ \ mathbb {s}^3 \ setminus 6^2_2 $。这些证据中的每一个都表明，前面建立的技术工具可以有效。
Neumann and Reid conjecture that there are exactly three knot complements which admit hidden symmetries. This paper establishes several results that provide evidence for the conjecture. Our main technical tools provide obstructions to having infinitely many fillings of a cusped manifold produce knot complements admitting hidden symmetries. Applying these tools, we show for any two-bridge link complement, at most finitely many fillings of one cusp can be covered by knot complements admitting hidden symmetries. We also show that the figure-eight knot complement is the unique knot complement with volume less than $6v_0 \approx 6.0896496$ that admits hidden symmetries. We then conclude with two independent proofs that among hyperbolic knot complements only the figure-eight knot complement can admit hidden symmetries and cover a filling of the two-bridge link complement $\mathbb{S}^3\setminus 6^2_2$. Each of these proofs shows that the technical tools established earlier can be made effective.
