Homotopy types of complements of 2arrangements 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 2arrangement 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712251
 arXiv:
 arXiv:math/9712251
 Bibcode:
 1997math.....12251M
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 Algebraic Geometry;
 52B30;
 57M05;
 57M25 (Primary);
 14M12;
 20F36 (Secondary)
 EPrint:
 LaTeX2e, 25 pages with 5 figures. Revised version, to appear in Topology