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

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

1997-12-16

arxiv.org/abs/math/9712251v2

Topology 39 (2000), no. 1, 61-88

Mathematics

Geometric Topology

LaTeX2e, 25 pages with 5 figures. Revised version, to appear in Topology

Scientific paper

10.1016/S0040-9383(98)00058-5

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.

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