论文标题
在Cayley-Persistence代数上
On the Cayley-persistence algebra
论文作者
论文摘要
在本文中，我们介绍了Cayley Digraph分级的持久（CO）同源性理论。我们提供了Cayley-Persistence对象的代数结构。具体而言，我们考虑了持久性（CO）同源性的模块结构，并显示有限生成的Cayley-Persistence模块的分解。此外，我们在Cayley-Persistence模块上介绍了持久性加上产品，并研究了有关持久性杯产物的扭曲结构。作为对多种多样的应用程序，我们表明持久（CO）同源性与基本类别的持续地图密切相关。
In this paper, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayley-persistence object. Specifically, we consider the module structure of persistent (co)homology and show the decomposition of a finitely generated Cayley-persistence module. Moreover, we introduce the persistence-cup product on the Cayley-persistence module and study the twisted structure with respect to the persistence-cup product. As an application on manifolds, we show that the persistent (co)homology is closely related to the persistent map of fundamental classes.
