Abstract: "We study the space of all extensions of a real hyperplance arrangement by a new pseudo-hyperplane, and, more generally, of an oriented matroid by a new element. The question whether this space has the homotopy type of a sphere is a special case of the 'Generalized Baues Problem&...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Sturmfels, Bernd 1962- (VerfasserIn), Ziegler, Günter M. 1963- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin 1991
Schriftenreihe:	Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1991,11
Schlagworte:	Combinatorial geometry Matroids
Zusammenfassung:	Abstract: "We study the space of all extensions of a real hyperplance arrangement by a new pseudo-hyperplane, and, more generally, of an oriented matroid by a new element. The question whether this space has the homotopy type of a sphere is a special case of the 'Generalized Baues Problem' of Billera, Kapranov & Sturmfels, via the Bohne-Dress Theorem on zonotopal tilings. We prove that the extension space is spherical for the class of strongly euclidean oriented matroids. This class includes the alternating matroids and all oriented matroids of rank at most 3 or of corank at most 2. In general it is not even known whether the extension space is connected. We show that the subspace of realizable extensions is always connected but not necessarily spherical."
Beschreibung:	20 S.