Detecting sphere boundaries of hyperbolic groups

Beeker, Benjamin¹ ; Lazarovich, Nir²

¹ Department of Mathematics, Haifa University, Jerusalem, Israel
² Department of Mathematics, ETH Zürich, Zürich, Switzerland

Geometry & topology, Tome 22 (2018) no. 1, pp. 439-470.

Résumé

We show that a one-ended simply connected at infinity hyperbolic group $G$ with enough codimension-$1$ surface subgroups has $\partial G\cong {\mathbb{S}}^2$. By work of Markovic (2013), our result gives a new characterization of virtually fundamental groups of hyperbolic $3$–manifolds.

Détail

DOI : 10.2140/gt.2018.22.439

Classification : 20F65, 20F67, 20H10
Keywords: $\mathrm{CAT}(0)$ cube complexes, hyperbolic groups, hyperbolic $3$–manifolds

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