WEAKLY EQUIVARIANT CLASSIFICATION OF SMALL COVERS OVER A PRODUCT OF SIMPLICIES

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.