论文标题
Bratteli图，翻译流及其$ C^*$ - 代数
Bratteli diagrams, translation flows and their $C^*$-algebras
论文作者
论文摘要
在[LT16]中，凯瑟琳·林赛（Kathryn Lindsey）和第二作者从双限时曲折图中构建了翻译表面。我们继续对这些表面进行调查。 [LT16]中给出的结构本质上是组合。在这里，我们提供了Bratteli图和表面的路径空间之间的明确联系，包括各种中间拓扑空间。这使我们能够在一些轻度的假设下将$ c^{*} $ - 代数与尾部等效相关的代数和表面的叶子。这也使我们可以将所涉及的$ c^{*} $的K理论联系起来。我们还详细处理有限属表面的情况，在这种情况下，Rauzy-Veech诱导过程（及其反向）提供了涉及的Bratteli图的明确结构。
In [LT16], Kathryn Lindsey and the second author constructed a translation surface from a bi-infinite Bratteli diagram. We continue an investigation into these surfaces. The construction given in [LT16] was essentially combinatorial. Here, we provide explicit links between the path space of the Bratteli diagram and the surface, including various intermediate topological spaces. This allows us to relate the $C^{*}$-algebras associated with tail equivalence on the Bratteli diagram and the foliation of the surface, under some mild hypotheses. This also allows us to relate the K-theory of the $C^{*}$-algebras involved. We also treat the case of finite genus surfaces in some detail, where the process of Rauzy-Veech induction (and its inverse) provide an explicit construction of the Bratteli diagrams involved.
