Algebraic & Geometric Topology

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

Joanna Jakus

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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].

Article information

Algebr. Geom. Topol., Volume 13, Number 5 (2013), 3031-3045.

Received: 7 February 2012
Revised: 23 April 2013
Accepted: 23 April 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F69: Asymptotic properties of groups

asymptotic hereditary asphericity free product HNN extension


Jakus, Joanna. Weak asymptotic hereditary asphericity for free product and HNN extension of groups. Algebr. Geom. Topol. 13 (2013), no. 5, 3031--3045. doi:10.2140/agt.2013.13.3031.

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