An arrangement of hyperplanes is a finite collection of codimension one subspaces in a finite-dimensional vector space. Arrangements occur in several branches of mathematics: combinatorics, braids, hypergeometric functions, reflection groups, singularities, and coding theory.

This book, based on lectures presented by the author at the CBMS Regional Conference held at Northern Arizona University in June 1988, provides the first introduction to the study of the topology of the complement of an arrangement in a complex vector space. The author discusses basic combinatorial tools, as well as algebras associated to the arrangement, differential forms, the cohomology and the homotopy type of the complement, free arrangements, and reflection arrangements. With a particular emphasis on topological aspects, this book provides an excellent introduction to current activity in this area.

Readership

Advanced graduate students and research mathematicians.

Table of Contents

• Introduction
• Combinatorics
• Combinatorial algebras
• Lattice homology
• The complement \(M(\mathcal A)\)
• The cohomology of \(M(\mathcal A)\)
• Differential forms
• The topology of \(M(\mathcal A)\)
• Free arrangements
• Reflection arrangements
• References