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)

  • 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
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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