m-Contiguity Distance
Algebraic Topology
2026-04-16 v3
Abstract
In this paper, we systematically develop the -contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of invariants that approximate the contiguity distance from below. The fundamental properties of -contiguity distance are established, including its behaviour under barycentric subdivision, under compositions, and a categorical product inequality. As applications of this theory, we define the -simplicial Lusternik-Schnirelmann category and the -discrete topological complexity, proving that each arises naturally as a special case of -contiguity distance.
Cite
@article{arxiv.2602.14680,
title = {m-Contiguity Distance},
author = {Nilay Ekiz Yazici and Nursultan Kuanyshov and Ayse Borat},
journal= {arXiv preprint arXiv:2602.14680},
year = {2026}
}