A manifold associated to a topological (n sub k) configuration - Bokowski, Jürgen (Ars mathematica contemporanea, 2014)
In the study of topological ?$(n_k)$? configurations in the projective plane we have ?$n$? pseudo-lines and ?$n$? points. Precisely ?$k$? of these points are incident with each pseudo-line and, vice versa, precisely ?$k$? pseudo-lines are incident with each point. We describe a non-orientable 2-manifold associated in a natural way to a topological ?$(n_k)$? configuration in the projective plane. Apart from being interesting in its own right, this manifold defines an equivalence class within topological configurations. It can be used to distinguish topological ?$(n_k)$? configurations.
Keywords: 2-manifold; konfiguracija; point-line configuration; pseudo-line; topologija