Combinatorial Morse theory and minimality of hyperplane arrangements

Using combinatorial Morse theory on the CW-complex S constructed in Salvetti [15] which gives the homotopy type of the complement to a complexified real arrangement of hyperplanes, we find an explicit combinatorial gradient vector field on S, such that S contracts over a minimal CW-complex. The existence of such minimal complex was proved before Dimca and Padadima [5] and Randell [14] and there exists also some description of it by Yoshinaga [19]. Our description seems much