Dowker Complexes and filtrations on self-relations

Autor:	Côté, Dominic Desjardins
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics 06A06 05C20 G.2.2
Druh dokumentu:	Working Paper
Popis:	Given a relation on $ X \times Y $, we can construct two abstract simplicial complexes called Dowker complexes. The geometric realizations of these simplicial complexes are homotopically equivalent. We show that if two relations are conjugate, then they have homotopically equivalent Dowker complexes. From a self-relation on $ X $, this is a directed graph, and we use the Dowker complexes to study their properties. We show that if two relations are shift equivalent, then, at some power of the relation, their Dowker complexes are homotopically equivalent. Finally, we define a new filtration based on Dowker complexes with different powers of a relation. Comment: 21 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.03739 Zobrazit plný text záznamu View this record from Arxiv