论文标题
过渡Coxeter 4-孔子的角色品种
Character varieties of a transitioning Coxeter 4-orbifold
论文作者
论文摘要
在2010年，Kerckhoff和Storm发现了一条双曲线4-Polytopes的途径，最终崩溃到了理想的右角cuboctahedron。这是通过在双曲线4空间等轴测组中包含离散反射组（右角Coxeter组）的变形表示的。最近，我们已经表明，可以将多型的路径扩展到抗DE保姆的几何形状，从而通过过渡的半管结构在天然相关的4孔叶上进行几何跃迁。 在本文中，我们研究了Kerckhoff和Storm的右角coxeter群的双曲线，反DE保姆和半管特征品种，附近每个发现的载体表示，包括对崩溃时出现的奇异性的描述。一个必不可少的工具是研究四个维度四个右角尖组的某些刚性特性。
In 2010, Kerckhoff and Storm discovered a path of hyperbolic 4-polytopes eventually collapsing to an ideal right-angled cuboctahedron. This is expressed by a deformation of the inclusion of a discrete reflection group (a right-angled Coxeter group) in the isometry group of hyperbolic 4-space. More recently, we have shown that the path of polytopes can be extended to Anti-de Sitter geometry so as to have geometric transition on a naturally associated 4-orbifold, via a transitional half-pipe structure. In this paper, we study the hyperbolic, Anti-de Sitter, and half-pipe character varieties of Kerckhoff and Storm's right-angled Coxeter group near each of the found holonomy representations, including a description of the singularity that appears at the collapse. An essential tool is the study of some rigidity properties of right-angled cusp groups in dimension four.
