Higher analogues of discrete topological complexity
Hilal Alabay, Ayşe Borat, Esra Cihangirli, Esma Dirican Erdal · Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas · 2024
Abstract In this paper, we introduce the nth discrete topological complexity and study its properties such as its relation with simplicial Lusternik–Schnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of n-th discrete topological complexity which is given by the nth usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.