Algebraic & Geometric Topology

A new characterization of Conrad's property for group orderings, with applications

Andrés Navas and Cristóbal Rivas

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We provide a pure algebraic version of the first-named author’s dynamical characterization of the Conrad property for group orderings. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof of a theorem first established by Linnell: an orderable group having infinitely many orderings has uncountably many. This proof is achieved by extending to uncountable orderable groups a result about orderings which may be approximated by their conjugates. This last result is illustrated by an example of an exotic ordering on the free group given by the third author in the Appendix.

Article information

Algebr. Geom. Topol., Volume 9, Number 4 (2009), 2079-2100.

Received: 3 March 2009
Revised: 28 August 2009
Accepted: 31 August 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 06F15: Ordered groups [See also 20F60] 20F60: Ordered groups [See mainly 06F15]
Secondary: 57S25: Groups acting on specific manifolds

group orders Conrad's property


Navas, Andrés; Rivas, Cristóbal. A new characterization of Conrad's property for group orderings, with applications. Algebr. Geom. Topol. 9 (2009), no. 4, 2079--2100. doi:10.2140/agt.2009.9.2079.

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