Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere

2025/02/13 by Douba, Sami, Lee, Gye-Seon, Marquis, Ludovic +1
#20F55 #20F65 #20F67 #22E40 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2502.09470

Abstract

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 50 reflections of ℍ⁴, and the other by a rotation of order 21 and a reflection of ℍ⁶. For each of them, we also locate convex cocompact subgroups with limit set a Menger curve.

Related

• Dynamical properties of convex cocompact actions in projective space
• Convex cocompact actions in real projective geometry
• Convex cocompactness for Coxeter groups
• Limit sets for convex cocompact groups in higher rank symmetric spaces
• Hyperbolic groups with planar boundaries