Non-geometric Veering Triangulations
Non-geometric Veering Triangulations
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非几何转向三角测量
DOI：
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发表时间：
2014
影响因子：
0.5
通讯作者：
Henry Segerman
中科院分区：
文献类型：
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作者：
C. Hodgson;Ahmad Issa;Henry Segerman
最近，Ian Agol引入了一类“转向”理想三角剖分，用于映射曲面的伪Anosov同胚环面，这些环面是沿着奇点打孔的。这些三角形有非常特殊的组合性质，和Agol问，如果这些是“几何”，即实现在完整的双曲度量与所有四面体积极取向。本文介绍了一个计算机程序转向，建立在托比霍尔的火车程序，从描述的同胚作为德恩扭曲的产品开始产生这些三角剖分。利用这一点，我们得到的第一个例子，非几何转向三角剖分，最小的例子，我们已经发现是一个三角与13个四面体。
Recently, Ian Agol introduced a class of “veering” ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and Agol asked if these are “geometric”, i.e. realized in the complete hyperbolic metric with all tetrahedra positively oriented. This article describes a computer program Veering, building on the program Trains by Toby Hall, for generating these triangulations starting from a description of the homeomorphism as a product of Dehn twists. Using this we obtain the first examples of non-geometric veering triangulations; the smallest example we have found is a triangulation with 13 tetrahedra.