Turkish Journal of Mathematics
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.
Contiguity distance, homotopic distance, topological complexity, Lusternik-Schnirelmann category
BORAT, AYŞE; PAMUK, MEHMETCİK; and VERGİLİ, TANE
"Contiguity distance between simplicial maps,"
Turkish Journal of Mathematics: Vol. 47:
2, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss2/17