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Weak asymptotic hereditary asphericity for free product and HNN extension of groups

Joanna Jakus

Algebraic & Geometric Topology 13 (2013) 3031–3045
Abstract

Asymptotic hereditary asphericity (AHA) is a coarse property of metric spaces and groups, introduced by T Januszkiewicz and J Swicatkowski in [Geom. Topol. 11 (2007) 727–758]. Conjecturally, this property is closed under amalgamated free products and HNN extensions over finite subgroups. We prove this conjecture for a slightly weaker property, weak asymptotic hereditary asphericity (AHA(-)), which is still strong enough for the purposes which AHA was used for in [Geom. Topol. 11 (2007) 727–758].

Keywords
asymptotic hereditary asphericity, free product, HNN extension
Mathematical Subject Classification 2000
Primary: 20F69
References
Publication
Received: 7 February 2012
Revised: 23 April 2013
Accepted: 23 April 2013
Published: 31 July 2013
Authors
Joanna Jakus
Instytut Matematyczny
Uniwersytet Wrocławski
pl. Grunwaldzki 2/4
50-384 Wrocław
Poland