Volume 14, issue 1 (2014)

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Asymptotic cones of HNN extensions and amalgamated products

Curtis Kent

Algebraic & Geometric Topology 14 (2014) 551–595
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.

Keywords
asymptotic cones, fundamental group, HNN extensions, amalgamated products
Mathematical Subject Classification 2010
Primary: 20F65, 20F69
Secondary: 57M07
References
Publication
Received: 16 October 2012
Revised: 9 January 2013
Accepted: 13 May 2013
Published: 23 January 2014
Authors
Curtis Kent
Mathematics Department
University of Toronto
Room 6290
40 St. George Street
Toronto, ON M5S 2E4
Canada
http://www.math.toronto.edu/cms/kent-curt/