Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc.

Published online July 28, 2022

Copyright © The Korean Mathematical Society.

weakly equivariant classification of small covers over a product of simplicies

Aslı Güçlükan İlhan and Sabri Kaan Gürbüzer

Dokuz Eylül University

Abstract

Given a dimension function ω, we introduce the notion of an ω-vector weighted digraph and an ω-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 Δ^ω(1) × · · · × Δ^ω(k) and the set of ω-equivalence classes of ω-vector weighted digraphs with k-labeled vertices where n = ω(1)+· · ·+ω(k). 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.

Keywords: Small cover, weakly equivariant homeomorphism, acyclic digraph

MSC numbers: 37F20; 57S10.

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