An operator algebraic perspective on Teichmüller dynamics.

我们的目标是研究非交换框架下的Teichmuller动力学。特别地，我们将研究将Teichmuller空间和动力学编码在单个代数结构中的Cuntz-Pimsner代数和群类群C*代数。这些C*代数上的k理论不变量变成了动力系统上的不变量，可以在动力环境中重新表述。该项目试图在不那么复杂的情况下利用以前的建筑来驱动我们的直觉。我们认为，Gadre等人的工作可能是一个关键的组成部分，他们对由典型循环引起的动力学进行了分类，这将在C*-代数上提供强连续自同构，并可能产生有趣的KMS平衡态和其他不变量。

We aim to study Teichmuller dynamics in a noncommutative framework. In particular, we will look at Cuntz-Pimsner and groupoid C*-algebras that encode both the Teichmuller space and dynamics in a single algebraic structure. K-theoretic Invariants on these C*-algebras become invariants on the dynamical systems that can be reformulated in a dynamical context. The project seeks to exploit previous constructions in less complicated situations to drive our intuition. We believe a critical component may come from the work of Gadre et al, where they classified dynamics arising from a canonical cocycle that will provide a strongly continuous automorphism on the C*-algebras and could give rise to interesting KMS Equilibrium states and other invariants.