A manifold associated to a topological (n_k) configuration

Jürgen Bokowski, Ricardo Strausz

Abstract


In the study of topological (nk) 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 (nk) 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 (nk) configurations.


Keywords


Point-line configuration, pseudo-line, 2-manifold

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DOI: https://doi.org/10.26493/1855-3974.241.7b5

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications