Character varieties of a transitioning Coxeter 4-orbifold

Groups, geometry, and dynamics

article

Stefano Riolo¹  Andrea Seppi² 

[1] Università di Bologna;Université Grenoble Alpes

关键词: Character varieties;    4-dimensional geometric structures;    geometric transition;    Coxeter orbifolds;    cusp rigidity;   

DOI  :  10.4171/ggd/653

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

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.

【 授权许可】

CC BY