Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

Corey Bregman; Merlin Incerti-Medici

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arXiv · 2109.05302

Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

Corey Bregman·Merlin Incerti-Medici

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Abstract

We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively curved manifold group is `wild' in the boundary. The proof is based on a notion of coarse upper curvature bounds in terms of barycenters and the careful study of interpolation in geodesic metric spaces.

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Corey Bregman, Merlin Incerti-Medici. 2021-09-11. Contractibility of boundaries of cocompact convex sets and embeddings of limit sets. https://arxiv.org/abs/2109.05302

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