Homotopy types of complements of 2-arrangements in R4

1997/12/31 by Daniel Matei, Alexander I. Suciu · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #alg-geom #math.AG #math.CO #math.GT #msc:14M12 #msc:20F36 #msc:52B30 #msc:57M05 #msc:57M25

paper · pdf · doi:10.1016/s0040-9383(98)00058-5

published as Topology 39 (2000), no. 1, 61-88 · LaTeX2e, 25 pages with 5 figures. Revised version, to appear in Topology

arxiv created 1998/08/14 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the homotopy types of complements of arrangements of n transverse planes in R⁴, 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 R⁴ 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.

Citations

• Characteristic varieties of arrangements

Cited by

• HALL INVARIANTS, HOMOLOGY OF SUBGROUPS, AND CHARACTERISTIC VARIETIES
• Limits with braid arrangements

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