Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3385
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
First Page
664
Last Page
677
Recommended Citation
BORAT, AYŞE; PAMUK, MEHMETCİK; and VERGİLİ, TANE
(2023)
"Contiguity distance between simplicial maps,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 17.
https://doi.org/10.55730/1300-0098.3385
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/17
