Algebraic & Geometric Topology

Spaces of orders of some one-relator groups

Juan Alonso and Joaquín Brum

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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.

Article information

Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4161-4185.

Received: 17 December 2017
Revised: 20 July 2018
Accepted: 29 July 2018
First available in Project Euclid: 18 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 06F15: Ordered groups [See also 20F60] 20F60: Ordered groups [See mainly 06F15]

left orders actions on the line one-relator groups


Alonso, Juan; Brum, Joaquín. Spaces of orders of some one-relator groups. Algebr. Geom. Topol. 18 (2018), no. 7, 4161--4185. doi:10.2140/agt.2018.18.4161.

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