Volume 22, issue 1 (2018)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Detecting sphere boundaries of hyperbolic groups

Benjamin Beeker and Nir Lazarovich

Geometry & Topology 22 (2018) 439–470
Abstract

We show that a one-ended simply connected at infinity hyperbolic group G with enough codimension-1 surface subgroups has GS2. 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