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.
1
Università di Bologna, Italy
2
Université Grenoble Alpes, France
Stefano Riolo; Andrea Seppi. Character varieties of a transitioning Coxeter 4-orbifold. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 779-842. doi: 10.4171/ggd/653
@article{10_4171_ggd_653,
author = {Stefano Riolo and Andrea Seppi},
title = {Character varieties of a transitioning {Coxeter} 4-orbifold},
journal = {Groups, geometry, and dynamics},
pages = {779--842},
year = {2022},
volume = {16},
number = {3},
doi = {10.4171/ggd/653},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/653/}
}
TY - JOUR
AU - Stefano Riolo
AU - Andrea Seppi
TI - Character varieties of a transitioning Coxeter 4-orbifold
JO - Groups, geometry, and dynamics
PY - 2022
SP - 779
EP - 842
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/653/
DO - 10.4171/ggd/653
ID - 10_4171_ggd_653
ER -
%0 Journal Article
%A Stefano Riolo
%A Andrea Seppi
%T Character varieties of a transitioning Coxeter 4-orbifold
%J Groups, geometry, and dynamics
%D 2022
%P 779-842
%V 16
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/653/
%R 10.4171/ggd/653
%F 10_4171_ggd_653
