论文标题
循环顺序和半偶像的空间
The space of circular orderings and semiconjugacy
论文作者
论文摘要
Linnell的工作表明，组的左端空间是有限的，要么是无数的，如果空间是有限的，则该组的同构类型是已知的---这就是所谓的塔拉林组。通过在一般环境中定义循环顺序的半偶像（也就是说，对于可能不对$ s^1 $起作用的组的任意循环顺序），我们可以将任何组的左顺序的子空间视为单个半偶像循环订购类别的单个半偶像类别。从这个角度来看，我们概括了Linnell的结果，以表明每个半偶像的循环订单类别都是有限的，也是无数的，并且当半偶像类是有限的时，该组具有规定的结构。我们还将左端的空间作为圆形订购空间的子空间进行研究，并解决了Baik和Samperton的问题。
Work of Linnell shows that the space of left-orderings of a group is either finite or uncountable, and in the case that the space is finite, the isomorphism type of the group is known---it is what is known as a Tararin group. By defining semiconjugacy of circular orderings in a general setting (that is, for arbitrary circular orderings of groups that may not act on $S^1$), we can view the subspace of left-orderings of any group as a single semiconjugacy class of circular orderings. Taking this perspective, we generalize the result of Linnell, to show that every semiconjugacy class of circular orderings is either finite or uncountable, and when a semiconjugacy class is finite, the group has a prescribed structure. We also investigate the space of left-orderings as a subspace of the space of circular orderings, addressing a question of Baik and Samperton.
