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Abstract
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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].
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Keywords
asymptotic hereditary asphericity, free product, HNN
extension
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Mathematical Subject Classification 2000
Primary: 20F69
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Publication
Received: 7 February 2012
Revised: 23 April 2013
Accepted: 23 April 2013
Published: 31 July 2013
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