Orlik–Solomon Algebras and de Rham Cohomology

Abstract

In this chapter we give the purely combinatorial definition of the Orlik–Solomon algebra of a hyperplane arrangement. A fundamental result says that this algebra is isomorphic to the cohomology algebra of the complex hyperplane arrangement complement. This is the first instance of a recurring theme which says that the topology is often determined by the combinatorics. A tensor product decomposition of the Orlik–Solomon algebra of a supersolvable arrangement, as well as an alternative view of the Orlik–Solomon algebra of a projective hyperplane arrangement, can also be found here.