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arXiv · 1512.00866

Sphere boundaries of hyperbolic groups

Benjamin Beeker·Nir Lazarovich
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Abstract

We show that a one-ended simply connected at infinity hyperbolic group $G$ with enough codimension-1 surface subgroups has $\partial G \cong \mathbb{S}^2$. Combined with a result of Markovic, our result gives a new characterization of virtually fundamental groups of hyperbolic 3-manifolds. Keywords: CAT(0) cube complexes, Hyperbolic groups, hyperbolic 3-manifolds.

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Benjamin Beeker, Nir Lazarovich. 2015-12-02. Sphere boundaries of hyperbolic groups. https://doi.org/10.2140/gt.2018.22.439

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