Codimension-1 subgroups of hyperbolic groups with spherical boundary

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• Corey Bregman (University of Southern Maine)
• Friday 06 May 2022, 13:45-14:45
• Zoom.

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Let G be a hyperbolic group with spherical boundary and let H≤G be a quasiconvex subgroup. We study which possible H can occur from both a geometric and topological perspective. In the geometric setting, if G is the fundamental group of a closed negatively curved manifold M and H is the fundamental group of a totally geodesic, codimension-1 submanifold N, then we provide sufficient conditions to promote the real hyperbolicity of N to that of M. In the topological direction, we consider the case where the boundary of G is S^3, and determine the possibilities for the Cech cohomology of the limit set of H. This is joint work with M. Incerti-Medici and B. Tshishiku.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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