On the coverings of Euclidean manifolds B-1 and B-2

摘要

There are only 10 Euclidean forms, that is flat closed three-dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of n-fold coverings over non-orientable Euclidean manifolds B-1 and B-2 and calculate the numbers of non-equivalent coverings of each type. We classify subgroups in the fundamental groups of B-1 and B-2 up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds B-1 and B-2 are uniquely determined among the other non-orientable forms by their homology groups H-1(B-1) = Z(2) x Z(2) and H-1 (B-2) = Z(2).