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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Dimca, A. (2017). Orlik–Solomon Algebras and de Rham Cohomology. In: Hyperplane Arrangements. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-56221-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-56221-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56220-9
Online ISBN: 978-3-319-56221-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)