Constructing Infinitely Many Geometric Triangulations Of The Figure Eight Knot Complement
Constructing Infinitely Many Geometric Triangulations Of The Figure Eight Knot Complement
复制标题
构造八字结补的无限多个几何三角剖分
DOI：
10.1090/proc/13076
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Aochen Duan
中科院分区：
文献类型：
--
作者：
Blake Dadd;Aochen Duan
本文考虑尖点双曲三维流形的“几何”理想三角剖分，即分解成正体积的理想双曲四面体。我们展示了无穷多个几何理想三角形的数字8结补。据我们所知，这是第一次构造一个尖点双曲三维流形的无穷多个几何三角剖分。相比之下，我们的方法并没有扩展到图8姐妹流形，它是未知的，如果有无限多个几何三角形的这个流形。
This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely many geometric triangulations of a cusped hyperbolic 3-manifold. In contrast, our approach does not extend to the figure eight sister manifold, and it is unknown if there are infinitely many geometric triangulations for this manifold.