Dynamics of isolated left orders
2020 年 72 巻 1 号 p. 185-211
詳細
2020 年 72 巻 1 号 p. 185-211
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 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 𝐵3 admits countably many isolated left orders which are not the automorphic images of the others.
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