论文标题
无限型表面上的层压和2填充射线
Laminations and 2-filling rays on infinite type surfaces
论文作者
论文摘要
无限型表面的循环图是朱丽叶·巴瓦德（Juliette Bavard）首先研究的无限直径双曲线图。无限型表面研究中的一个重要开放问题是将循环图的边界描述为地球层压的空间。我们通过在无限型表面上构建2填充射线的第一个示例来解决这个问题。这种射线会积聚在某种意义上填充的大地层压板上，但没有足够强的特性，无法与环图边界的点相对应。我们使用动手组合方法和使用扁平表面的火车轨道和自动形态的方法提供多个结构。此外，我们的方法足够强大，可以描述具有某些其他基本特性的所有2填充射线，并且可以产生许多不同的映射类组轨道。
The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite type surfaces is to describe the boundary of the loop graph as a space of geodesic laminations. We approach this problem by constructing the first examples of 2-filling rays on infinite type surfaces. Such rays accumulate onto geodesic laminations which are in some sense filling, but without strong enough properties to correspond to points in the boundary of the loop graph. We give multiple constructions using both a hands-on combinatorial approach and an approach using train tracks and automorphisms of flat surfaces. In addition, our approaches are sufficiently robust to describe all 2-filling rays with certain other basic properties as well as to produce uncountably many distinct mapping class group orbits.
