#### Volume 11, issue 3 (2007)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Combinatorial Morse theory and minimality of hyperplane arrangements

### Mario Salvetti and Simona Settepanella

Geometry & Topology 11 (2007) 1733–1766
 arXiv: 0705.2874
##### Abstract

Using combinatorial Morse theory on the CW–complex $S$ 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 $S$, such that $S$ 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.

##### Keywords
Morse theory, arrangements, combinatorics
##### Mathematical Subject Classification 2000
Primary: 32S22
Secondary: 52C35, 32S50