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January, 2020 Dynamics of isolated left orders
Shigenori MATSUMOTO
J. Math. Soc. Japan 72(1): 185-211 (January, 2020). DOI: 10.2969/jmsj/77357735

Abstract

A left order of a countable group $G$ is called isolated if it is an isolated point in the compact space $LO(G)$ of all the left orders of $G$. We study properties of a dynamical realization of an isolated left order. Especially we show that it acts on $\mathbb{R}$ cocompactly. As an application, we give a dynamical proof of the Tararin theorem which characterizes those countable groups which admit only finitely many left orders. We also show that the braid group $B_3$ admits countably many isolated left orders which are not the automorphic images of the others.

Funding Statement

The author was partially supported by Grant-in-Aid for Scientific Research (C) No. 18K03312.

Citation

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Shigenori MATSUMOTO. "Dynamics of isolated left orders." J. Math. Soc. Japan 72 (1) 185 - 211, January, 2020. https://doi.org/10.2969/jmsj/77357735

Information

Received: 17 February 2017; Revised: 21 September 2018; Published: January, 2020
First available in Project Euclid: 27 August 2019

zbMATH: 07196503
MathSciNet: MR4055461
Digital Object Identifier: 10.2969/jmsj/77357735

Subjects:
Primary: 20F65
Secondary: 20F05

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 1 • January, 2020
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