On Heaviside functions of a hyperplane configuration. (Russian) Zbl 0647.32013

Varchenko, A. N.; Gel’fand, I. M.

Funkts. Anal. Prilozh. 21, No. 4, 1-18 (1987).

Let M be the complement in \({\mathbb{R}}^ n \)to the union of a finite family of hyperplanes, \(M_{{\mathbb{C}}}\) be the complement in \({\mathbb{C}}^ n \)to the union of corresponding complexified hyperplanes. The paper is devoted to the comparison of properties of the ring P of integer-valued continuous functions on M and the ring H of cohomology of \(M_{{\mathbb{C}}}\). It gives, in particular, a new proof of some results of P. Orlik and L. Solomon [Invent. Math. 56, 167-189 (1980; Zbl 0432.14016)].

Reviewer: S.I.Gel’fand

MSC:

32C25

Analytic subsets and submanifolds

Keywords:

complement of hyperplanes; integer-valued continuous functions; cohomology