WEAKLY EQUIVARIANT CLASSIFICATION OF SMALL COVERS OVER A PRODUCT OF SIMPLICIES

GÜÇLÜKAN İLHAN A., GÜRBÜZER S. K.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.59, no.5, pp.963-986, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.4134/jkms.j220104
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.963-986
  • Keywords: Small cover, weakly equivariant homeomorphism, acyclic digraph
  • Dokuz Eylül University Affiliated: Yes

Abstract

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.