Number of nonequivalent coverings over a nonorientable compact surface
Let S be a compact surface and \(\pi\) : \(T\to S\) and \(\pi\) ': T'\(\to S\) two coverings over S. We say that \(\pi\) and \(\pi\) ' are equivalent if there exists a homeomorphism \(h: T\to T'\) such that \(\pi =\pi '\circ h\). The first author [Sib. Mat. Zh. 23, No.3, 155-160 (1982; Zbl 0513.30036)] had obtained the exact formulas for the number of non-equivalent coverings over orientable surface S having a given multiplicity. This result can be considered as a partial solution of the Hurwitz enumeration problem completely solved by the same author [Sib. Mat. Zh. 25, No.4(146), 120-142 (1984; reviewed above)]. In the present paper the number of subgroups of a given index in the fundamental group of non-orientable surface S are determined and the number of non-equivalent coverings over S of a given multiplicity are obtained.
scientific article; zbMATH DE number 3964350