Algebraic & Geometric Topology

Spaces of orders of some one-relator groups

Juan Alonso and Joaquín Brum

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

Permanent link to this document
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

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

Keywords
left orders actions on the line one-relator groups

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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