## Algebraic & Geometric Topology

### Spaces of orders of some one-relator groups

#### Abstract

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

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

Dates
Revised: 20 July 2018
Accepted: 29 July 2018
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.agt/1545102069

Digital Object Identifier
doi:10.2140/agt.2018.18.4161

Mathematical Reviews number (MathSciNet)
MR3892243

Zentralblatt MATH identifier
07006389

#### Citation

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. https://projecteuclid.org/euclid.agt/1545102069

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