2:00 pm Wednesday, March 4, 2020
Junior Topology: Discrete linear groups generated by reflections by Florian Stecker in RLM 12.166
Given a convex polytope K, what is the group generated by the reflections along its faces? When is it discrete and produces a tiling of some convex set by copies of K? Vinberg gives simple conditions for this in Euclidean, hyperbolic, spherical and (most importantly) projective space, and shows that these groups can be easily parametrized. Although these results are already about 50 years old, they are still being actively used as a source of examples for discrete subgroups of PGL(n,R). Submitted by
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