WEAKLY EQUIVARIANT CLASSIFICATION OF SMALL COVERS OVER A PRODUCT OF SIMPLICIES

GÜÇLÜKAN İLHAN A., GÜRBÜZER S. K.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.59, sa.5, ss.963-986, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.4134/jkms.j220104
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.963-986
  • Anahtar Kelimeler: Small cover, weakly equivariant homeomorphism, acyclic digraph
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Given a dimension function omega, we introduce the notion of an omega-vector weighted digraph and an omega-equivalence between them. Then we establish a bijection between the weakly (Z/2)(n)-equivariant homeomorphism classes of small covers over a product of simplices Delta(omega(1)) x center dot center dot center dot x Delta(omega(m)) and the set of omega-equivalence classes of omega-vector weighted digraphs with m-labeled vertices, where n is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly (Z/2)(n)-equivariant homeomorphism classes of small covers over a product of three simplices.