Ramified coverings of nonorientable surfaces by orientable surfaces with prescribed boundary projection
Consider a compact surface \(N\), without boundary, together a collection \(\beta_{1}\),\dots, \(\beta_{v}\), of closed curves on it. The authors investigate the problem of finding conditions on the above loops in order to find a compact surface with boundary \({\overline M}=M \cup \partial(M)\) and a continuous map \(p:{\overline M} \to N\) so that \(p(\partial(M))=\beta_{1} \cup \cdots \cup \beta_{v}\). They proceed to find such a condition under the hypothesis that \(v=1\) and \(N\) is nonorientable.
scientific article; zbMATH DE number 1228280