Topology of plane arrangements and their complements

TL;DR

This paper provides a comprehensive overview of the topological theory of affine plane arrangements, covering key concepts, methods, and applications in geometry, topology, and related fields.

Contribution

It offers a detailed glossary of notions and methods, emphasizing geometric explanations and connecting various topological and algebraic tools related to plane arrangements.

Findings

Summarizes key topological concepts and methods for affine plane arrangements.

Highlights applications in differential topology and related fields.

Provides a unified framework for understanding arrangements and their complements.

Abstract

This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik--Solomon rings, Salvetti complex, matroids, Spanier--Whitehead duality, twisted homology groups, monodromy theory and multidimensional hypergeometric functions. The emphasis on the most geometrical explanation is done; applications and analogies in the differential topology are outlined.