Geometry & Topology
- Geom. Topol.
- Volume 11, Number 3 (2007), 1733-1766.
Combinatorial Morse theory and minimality of hyperplane arrangements
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.
Geom. Topol., Volume 11, Number 3 (2007), 1733-1766.
Received: 28 March 2007
Accepted: 18 July 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35]
Secondary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants
Salvetti, Mario; Settepanella, Simona. Combinatorial Morse theory and minimality of hyperplane arrangements. Geom. Topol. 11 (2007), no. 3, 1733--1766. doi:10.2140/gt.2007.11.1733. https://projecteuclid.org/euclid.gt/1513799909