The Morse complex of a line arrangement (Q2518368)

The authors compute efficiently the Abelian local system homology of the complement of a complex line arrangement \({\mathcal A}\) in \({\mathbb C}^2\), assuming that \({\mathcal A}\) is defined over \({\mathbb R}\). The result is a variant of the calculation in [\textit{M. Salvetti} and \textit{S. Settepanella}, Geom. Topol. 11, 1733--1766 (2007; Zbl 1134.32010)], with an in practice much simpler form of the differential in the Morse complex that computes the homology. It is mainly because of being in dimension~\(2\) that the improvement is possible; it is still too notationally complex to repeat here. Nevertheless the authors are able to demonstrates its relative ease of use in practice in a number of examples.