2026/08/03 by Nilay Ekiz Yazici, Nursultan Kuanyshov, Ayse Borat
Mathematics · #math.AT #msc:55M30 #msc:55U10 #msc:55U05
arxiv created 2026/08/03 · arxiv updated 2026/08/04
In this paper, we introduce the notion of sequential m-contiguity distance for finitely many simplicial maps as a higher analogue of contiguity distance. This invariant generalizes both higher contiguity distance and m-contiguity distance, and provides a combinatorial counterpart of sequential m-homotopic distance. We investigate its fundamental properties, including invariance under strong homotopy type, behaviour under compositions, categorical products, and barycentric subdivision. Moreover, we define sequential m-discrete topological complexity of simplicial complexes. As applications, we characterise this invariant (along with m-simplicial LS category) in terms of sequential m-contiguity distance and prove that they are invariants of strong homotopy type. Furthermore, we establish inequalities relating m-simplicial LS category and m-discrete sequential topological complexity, extending classical results from topological complexity theory to the simplicial and m-dimensional setting.