An application of non-positively curved cubings of alternating links
An application of non-positively curved cubings of alternating links
复制标题
交替连杆非正曲立方体的应用
DOI：
10.1090/proc/13918
复制
发表时间：
2018
影响因子：
1
通讯作者：
Yokota Yoshiyuki
中科院分区：
文献类型：
--
作者：
Sakuma Makoto;Yokota Yoshiyuki
通过使用素数交替链接外部的非正曲立方，我们证明了从简化交替图导出的它们的补集的某些理想三角剖分是非退化的，从某种意义上说，没有一条边相对于其端点与外围弧是同伦的。这保证了双曲交替连接的三角剖分的双曲方程具有与完整双曲结构相对应的解。由于本文考虑的理想三角剖分经常用于体积猜想的研究，因此该结果对体积猜想具有潜在的应用价值。参考
By using non-positively curved cubings of prime alternating link exteriors, we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of the edges is homotopic relative its endpoints to a peripheral arc. This guarantees that the hyperbolicity equations for those triangulations for hyperbolic alternating links have solutions corresponding to the complete hyperbolic structures. Since the ideal triangulations considered in this paper are often used in the study of the volume conjecture, this result has a potential application to the volume conjecture. References