Contiguity distance between simplicial maps


Borat A., PAMUK M., VERGİLİ T.

TURKISH JOURNAL OF MATHEMATICS, vol.47, no.2, pp.664-677, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3385
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.664-677
  • Keywords: Contiguity distance, homotopic distance, topological complexity, Lusternik-Schnirelmann category, LUSTERNIK-SCHNIRELMANN CATEGORY
  • Karadeniz Technical University Affiliated: Yes

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.