论文标题
有限呈现的左订购怪物
Finitely presented left orderable monsters
论文作者
论文摘要
左订购的怪物是一个有限生成的左订购组，其所有无固定点的操作均为近端：该动作是半偶联的，因此，对于每个有界的间隔$ i $ and open Interval $ j $，该元件都将$ i i $ $ i $ $ j $发送到$ j $。纳瓦斯在2018年的ICM讲话中询问了左有序怪物的存在。到目前为止，有几个示例，所有示例都是有限生成的，但不能有限地呈现。我们提供了有限呈现的左订购怪物的第一个示例，甚至是$ f_ \ infty $的类型。结构本身是基本的，这些群体满足了将它们与以前的示例分开的其他几个属性：它们并不简单，它们在圆圈上的作用最低，并且它们具有同质的准牙作用的无限维空间。我们的构造足够灵活，可以生成有限呈现（和类型$ f _ {\ infty} $）的许多同构类别的左订购怪物。
A left orderable monster is a finitely generated left orderable group all of whose fixpoint-free actions on the line are proximal: the action is semiconjugate to a minimal action so that for every bounded interval $I$ and open interval $J$, there is a group element that sends $I$ into $J$. In his 2018 ICM address, Navas asked about the existence of left orderable monsters. By now there are several examples, all of which are finitely generated but not finitely presentable. We provide the first examples of left orderable monsters that are finitely presentable, and even of type $F_\infty$. The construction itself is elementary, and these groups satisfy several additional properties separating them from the previous examples: they are not simple, they act minimally on the circle, and they have an infinite-dimensional space of homogeneous quasimorphisms. Our construction is flexible enough that it produces infinitely many isomorphism classes of finitely presented (and type $F_{\infty}$) left orderable monsters.
