Topology of plane arrangements and their complements

2014/07/27 by V. A. Vassiliev, Vassiliev, Victor A. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1407.7236

openalex publication_date 2014/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• Decomposition in Coxeter-chambers of the configuration space of d marked points on the complex plane

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