Asymptotic cones of HNN extensions and amalgamated products

Kent, Curtis¹

¹Mathematics Department, University of Toronto, Room 6290, 40 St. George Street, Toronto, ON M5S 2E4, Canada

Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 551-595

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.551

Classification : 20F65, 20F69, 57M07
Keywords: asymptotic cones, fundamental group, HNN extensions, amalgamated products

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