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On the Cayley-persistence algebra

  • 演讲者:刘健(河北师范大学,北京雁栖湖应用数学研究院)

  • 时间:2022-09-16 16:30-17:30

  • 地点:腾讯会议ID 865-807-509

Abstract

In this talk, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayleypersistence object. Specifically, we consider the module structure of persistent (co)homology and show the decomposition of a finitely generated Cayleypersistence 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.