On the Cayley-persistence algebra
Algebraic Topology
2022-08-18 v4
Abstract
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.
Cite
@article{arxiv.2205.10796,
title = {On the Cayley-persistence algebra},
author = {Wanying Bi and Jingyan Li and Jian Liu and Jie Wu},
journal= {arXiv preprint arXiv:2205.10796},
year = {2022}
}