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math.GT2025
On reflections of congruence hyperbolic manifolds
Sami Douba, Franco Vargas Pallete
We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed poi…
math.GT2025
Zariski-Closures of Linear Reflection Groups
Jacques Audibert, Sami Douba, Gye-Seon Lee +1
We give necessary and sufficient conditions for a linear reflection group in the sense of Vinberg to be Zariski-dense in the ambient projective general linear group. As an applicat…
math.GT2025
Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere
Sami Douba, Gye-Seon Lee, Ludovic Marquis +1
We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by reflections of $\ma…