Volume 18, issue 7 (2018)

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Spaces of orders of some one-relator groups

Juan Alonso and Joaquín Brum

Algebraic & Geometric Topology 18 (2018) 4161–4185

We show that certain left-orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general left-orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line.

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left orders, actions on the line, one-relator groups
Mathematical Subject Classification 2010
Primary: 06F15, 20F60
Received: 17 December 2017
Revised: 20 July 2018
Accepted: 29 July 2018
Published: 11 December 2018
Juan Alonso
Facultad de Ciencias
Universidad de la República
Joaquín Brum
Facultad de Ingenieria
Universidad de la República