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.
- Publication:
-
arXiv Mathematics e-prints
- 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)
- E-Print:
- LaTeX2e, 25 pages with 5 figures. Revised version, to appear in Topology