Asymptotic cones of HNN extensions and amalgamated products

Kent, Curtis

doi:10.2140/agt.2014.14.551

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Asymptotic cones of HNN extensions and amalgamated products

Curtis Kent

Algebraic & Geometric Topology 14 (2014) 551–595

DOI: 10.2140/agt.2014.14.551

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/

Volume 14, issue 1 (2014)