论文标题
持续同源性的Galois连接
Galois Connections in Persistent Homology
论文作者
论文摘要
我们为Galois连接介绍了一种持续同源性的新语言。与传统方法相比，该语言具有两个主要优势。首先，它简化和统一了中心概念，例如交织和匹配。其次，它提供了对Rota的Galois Connection定理的访问权限，这是一种强大的工具，具有许多潜在的应用拓扑应用程序。为了说明这一点，我们使用Rota的Galois Connection定理为瓶颈稳定性定理提供了更容易的证明。最后，我们使用这种语言来建立多参数持续图的各种概念之间的关系。
We present a new language for persistent homology in terms of Galois connections. This language has two main advantages over traditional approaches. First, it simplifies and unifies central concepts such as interleavings and matchings. Second, it provides access to Rota's Galois connection theorem -- a powerful tool with many potential applications in applied topology. To illustrate this, we use Rota's Galois connection theorem to give a substantially easier proof of the bottleneck stability theorem. Finally, we use this language to establish relationships between various notions of multiparameter persistence diagrams.
