Pakula, Lewis Regions cut by arrangements of topological spheres. (English) Zbl 0799.52010 Can. Math. Bull. 36, No. 2, 241-244 (1993). An arrangement \(A\) of pseudohyperplanes in \(\mathbb{R}^ n\) is the image, under stereographic projection, of a collection of proper subsets \(A_ 1, \dots, A_ k\) of a topological \(n\)-sphere \(S^ n\) having spherical intersections such that(i) each \(A_ i\) is a topological \((n-1)\)-sphere containing the pole \(N\),(ii) for \(I \subseteq \{1, \dots, k\}\), \(I \neq \emptyset\), either \(\cap_{i \in I} (A_ i) = \{N\}\) or \(\cap_{i \in I} (A_ i)\) is a topological sphere of dimension \(\geq n - | I | \geq 0\).By showing that the complement components are homologically trivial, the author extends the Wiener-Zaslavsky formula on the number of regions induced by \(A\) in terms of intersection degeneracies. Reviewer: H.Martini (Chemnitz) Cited in 1 Document MSC: 52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 51M20 Polyhedra and polytopes; regular figures, division of spaces 05A99 Enumerative combinatorics Keywords:pseudoline arrangements; pseudohyperplane arrangements; cohomology; stereographic projection; Wiener-Zaslavsky formula PDFBibTeX XMLCite \textit{L. Pakula}, Can. Math. Bull. 36, No. 2, 241--244 (1993; Zbl 0799.52010) Full Text: DOI