Extension Spaces of Oriented Matriods.
Please always quote using this URN: urn:nbn:de:0297-zib-618
- We study the space of all extensions of a real hyperplane 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.
| Author: | Bernd Sturmfels, Günter M. Ziegler |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1991/10/23 |
| Series (Serial Number): | ZIB-Report (SC-91-11) |
| ZIB-Reportnumber: | SC-91-11 |
| Published in: | Appeared in: Discrete and Computational Geometry 10 (1993) pp. 23-45 |
