an:00034074
Zbl 0754.52003
Bj??rner, Anders; Ziegler, G??nter M.
Combinatorial stratification of complex arrangements
EN
J. Am. Math. Soc. 5, No. 1, 105-149 (1992).
00159058
1992
j
52C35 57N80 05B35 32S60
oriented matroid; matroid stratification; regular cell complex; pseudo- arrangement
An arrangement of complex hyperplanes of \(\mathbb{C}^ d\) through the origin is encoded by certain combinatorial data in terms of complex signs, posets, matroids, and stratifications. The topology of such an arrangement and its complement is studied, in particular for its link in the sphere \(S^{2d-1}\). Somehow, this corresponds to results by J. Milnor and E. Brieskorn on complex singularities. Especially it is shown that for \(d\geq 4\) the link of an arrangement has the homotopy type of a wedge of spheres. Alexander duality provides a relation for the homology and cohomology. Finally, an outline is given for more general types of arrangements.
W.K??hnel (Duisburg)