---
abstract: 'We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras, higher homotopy groups, cohomology rings, twisted homology with rank $1$ complex coefficients, and Milnor fibers.'
address: |
    Inst. of Math. Simion Stoilow\
    P.O. Box 1-764\
    RO-014700 Bucharest, Romania
author:
- 'Anca Daniela Măcinic$^*$'
title: A Survey of Combinatorial Aspects in the Topology of Complex Hyperplane Arrangements
---

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Introduction {#sect:intro}
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By a hyperplane arrangement ${{\mathcal A}}$ we understand in what follows either a collection $\{ H_1,\dots, H_n \}$ of codimension one subspaces in a finite dimensional vector space $V$ or the subspace of the ambient space $V$ given by their union. We consider here only arrangements in [*complex*]{} affine spaces.

The starting point in the study of complex hyperplane arrangements was the braid arrangement, ${{\mathcal A}}=\{H_{ij}=\operatorname{Ker}(z_i-z_j)\;|\; 1\le i\neq j \le n \} \subset {\mathbb{C}}^n$. The results obtained for the complement $M_{{{\mathcal A}}}= \{z \in {\mathbb{C}}^n\;|\; z_i \neq z_j\; \forall i \neq j\}$ – factorization of the Poincar' e polynomial and the presentation of the cohomology algebra in terms of generators and relations (Arnold [@Ar]), or 