Abstract
Using combinatorial Morse theory on the CW–complex constructed by Salvetti [Invent. Math. 88 (1987) 603–618] which gives the homotopy type of the complement to a complexified real arrangement of hyperplanes, we find an explicit combinatorial gradient vector field on , such that contracts over a minimal CW–complex.
The existence of such minimal complex was proved before Dimca and Padadima [Ann. of Math. (2) 158 (2003) 473–507] and Randell [Proc. Amer. Math. Soc. 130 (2002) 2737–2743] and there exists also some description of it by Yoshinaga [Kodai Math. J. (2007)]. Our description seems much more explicit and allows to find also an algebraic complex computing local system cohomology, where the boundary operator is effectively computable.
Citation
Mario Salvetti. Simona Settepanella. "Combinatorial Morse theory and minimality of hyperplane arrangements." Geom. Topol. 11 (3) 1733 - 1766, 2007. https://doi.org/10.2140/gt.2007.11.1733
Information