Algebraic & Geometric Topology

Asymptotic cones of HNN extensions and amalgamated products

Curtis Kent

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715811

Digital Object Identifier
doi:10.2140/agt.2014.14.551

Mathematical Reviews number (MathSciNet)
MR3158768

Zentralblatt MATH identifier
1327.20046

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

Keywords
asymptotic cones fundamental group HNN extensions amalgamated products

Citation

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. https://projecteuclid.org/euclid.agt/1513715811


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