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Sphere boundaries of hyperbolic groups (1512.00866v2)
Published 2 Dec 2015 in math.GR
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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