Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations
Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations
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理想三角剖分的伪展开图 I：基本边和广义双曲粘合方程
DOI：
10.1090/conm/560/11093
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Stephan Tillmann
中科院分区：
文献类型：
--
作者：
Henry Segerman;Stephan Tillmann
令 N 为具有理想三角剖分的拓扑有限、可定向 3 流形。我们证明，如果双曲粘合方程有解，那么三角剖分中的所有边都是必不可少的。该结果被扩展到双曲粘合方程的推广，这使得能够在 N 上构造双曲锥流形结构，并在三角剖分的 1-骨架中包含奇异轨迹。
Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a generalisation of the hyperbolic gluing equations, which enables the construction of hyperbolic cone-manifold structures on N with singular locus contained in the 1-skeleton of the triangulation.