Detecting sphere boundaries of hyperbolic groups

Beeker, Benjamin; Lazarovich, Nir

doi:10.2140/gt.2018.22.439

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Detecting sphere boundaries of hyperbolic groups

Benjamin Beeker and Nir Lazarovich

Geometry & Topology 22 (2018) 439–470

DOI: 10.2140/gt.2018.22.439

Abstract

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

Keywords

$\mathrm{CAT}(0)$ cube complexes, hyperbolic groups, hyperbolic $3$–manifolds

Mathematical Subject Classification 2010

Primary: 20F65, 20F67, 20H10

References

Publication

Received: 14 February 2016

Revised: 16 February 2017

Accepted: 28 April 2017

Published: 31 October 2017

Proposed: Martin Bridson

Seconded: Walter Neumann, Peter Teichner

Authors

Benjamin Beeker
Department of Mathematics Haifa University Jerusalem Israel

Nir Lazarovich
Department of Mathematics ETH Zürich Zürich Switzerland

Volume 22, issue 1 (2018)