Contiguity distance between simplicial maps

Borat A., PAMUK M., VERGİLİ T.

TURKISH JOURNAL OF MATHEMATICS, cilt.47, sa.2, ss.664-677, 2023 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.55730/1300-0098.3385
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.664-677
  • Anahtar Kelimeler: Contiguity distance, homotopic distance, topological complexity, Lusternik-Schnirelmann category, LUSTERNIK-SCHNIRELMANN CATEGORY
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.