Contiguity distance between simplicial maps

Authors: AYŞE BORAT, MEHMETCİK PAMUK, TANE VERGİLİ

Abstract: For simplicial complexes and simplicial maps, the notion of being in the same contiguity class is defined as the discrete version of homotopy. In this paper, we study the contiguity distance, $SD$, between two simplicial maps adapted from the homotopic distance. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion. Moreover, we present the behaviour of $SD$ under the barycentric subdivision, and its relation with strong collapsibility of a simplicial complex.

Keywords: Contiguity distance, homotopic distance, topological complexity, Lusternik-Schnirelmann category

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