Homotopy types of complements of 2-arrangements in R^4

Abstract

We study the homotopy types of complements of arrangements of n transverse planes in R^4, obtaining a complete classification for n <= 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R^4 is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the characteristic varieties of the complement. The nature of these varieties illustrates the difference between real and complex arrangements.

arXiv commentLaTeX2e, 25 pages with 5 figures. Revised version, to appear in Topology

References in corpus (3)

• Geometry of cohomology support loci for local systems I
• Characteristic varieties of arrangements
• Cohomology of the Orlik-Solomon algebras and local systems

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