Algebraic & Geometric Topology

Asymptotic cones of HNN extensions and amalgamated products

Curtis Kent

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Gromov asked whether an asymptotic cone of a finitely generated group was always simply connected or had uncountable fundamental group. We prove that Gromov’s dichotomy holds for asymptotic cones with cut points, as well as HNN extensions and amalgamated products where the associated subgroups are nicely embedded. We also show a slightly weaker dichotomy for multiple HNN extensions of free groups.

Article information

Algebr. Geom. Topol., Volume 14, Number 1 (2014), 551-595.

Received: 16 October 2012
Revised: 9 January 2013
Accepted: 13 May 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F69: Asymptotic properties of groups
Secondary: 57M07: Topological methods in group theory

asymptotic cones fundamental group HNN extensions amalgamated products


Kent, Curtis. Asymptotic cones of HNN extensions and amalgamated products. Algebr. Geom. Topol. 14 (2014), no. 1, 551--595. doi:10.2140/agt.2014.14.551.

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