Extension spaces of oriented matroids
type: Item
instance of: scholarly article
title: Extension spaces of oriented matroids
zbMATH Open document ID: 0783.52009
DOI: 10.1007/BF02573961
author: Bernd Sturmfels
author: Günter M. Ziegler
published in: Discrete \& Computational Geometry
publication date: 1993-09-20T00:00:00Z
full work available at URL: https://eudml.org/doc/131258
review text: Extension spaces \({\mathcal E}(M)\) of realizable oriented matroids \(M\) are of key importance in the theory of discrete models of Grassmannians (MacPhersonians). The main problem in this context is to prove sphericity of \({\mathcal E}(M)\), and this question is seen as a special case of the so- called ``Generalized Baues Problem'' of Billera, Kapranov and Sturmfels. The extension space is of course interesting in its own right, both as an invariant of \(M\) and because of its relations to other objects and constructions, say to higher Bruhat orders of Manin and Schechtman. The authors prove that the extension space is indeed spherical for the class of strongly Euclidean oriented matroids. This class includes the alternating matroids and all oriented matroids of rank at most 3 and corank at most 2. They also show that the subspace of realizable extensions is always connected but not necessarily spherical.
reviewed by: Rade Živaljević
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 279757
zbMATH Keywords: MacPhersonians
zbMATH Keywords: oriented matroids
zbMATH Keywords: Grassmannians
zbMATH Keywords: extension space
MaRDI profile type: Publication
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OpenAlex ID: W2160283861
description: scientific article