论文标题
无限层次的横向测量
Transverse measures to infinite type laminations
论文作者
论文摘要
我们研究了无限型双曲表面上固定的大地层压层的横向测量锥。在公制上的简单假设下，我们将该锥体的明确描述作为有限维锥的逆极限。我们研究了横向测量锥何时接受基础的问题，并表明存在许多层压层的基础。此外，基础是（通常是无限维）的单纯形（称为Choquet单纯形），可以明确地描述为有限维基的逆限制。我们表明，在任何固定的无限型双曲表面上，每个choquet单纯形都作为某种层压的基础。我们使用我们的倒数限制描述和新的大地层层化结构，为具有外来特性的其他明确示例提供了其他明确的例子。
We study the cone of transverse measures to a fixed geodesic lamination on an infinite type hyperbolic surface. Under simple hypotheses on the metric, we give an explicit description of this cone as an inverse limit of finite-dimensional cones. We study the problem of when the cone of transverse measures admits a base and show that such a base exists for many laminations. Moreover, the base is a (typically infinite-dimensional) simplex (called a Choquet simplex) and can be described explicitly as an inverse limit of finite-dimensional simplices. We show that on any fixed infinite type hyperbolic surface, every Choquet simplex arises as a base for some lamination. We use our inverse limit description and a new construction of geodesic laminations to give other explicit examples of cones with exotic properties.
