On the fundamental group of the complement of arrangements
The author describes a method to compute a presentation of the fundamental group of the complement of the union of a finite arrangement of hyperplanes in \(\mathbb{C}^n\) having real defining equations. The method involves the notion of ``1-codimensionally regular CW-semicomplex'', introduced in previous work of author. This decomposition of the hyperplane complement bears some similarity to known regular CW-complexes associated with arrangements, but is smaller, retaining just enough structure for the fundamental group calculation. The author's approach does not require the choice of a generic 3-dimensional section, as in the Randell-Arvola presentation. The resulting presentation does not appear to differ substantially from the presentation obtained by \textit{M. Salvetti} [Invent. Math. 88, 603-618 (1987; Zbl 0594.57009)].
scientific article; zbMATH DE number 729234