Poincar\'e Duality for Generalized Persistence Diagrams of (co)Filtrations

Autor:	Patel, Amit, Rask, Tatum
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Computer Science - Computational Geometry Mathematics - Category Theory
Zdroj:	Journal of Applied and Computational Topology (2024)
Druh dokumentu:	Working Paper
DOI:	10.1007/s41468-023-00159-0
Popis:	We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincar\'e duality between their generalized persistence diagrams. A heavy emphasis is placed on the recent discovery of functoriality of the generalized persistence diagram and its connection to Rota's Galois Connection Theorem. Comment: Final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.14610 Zobrazit plný text záznamu View this record from Arxiv