Overview

The author considers the concept of triangulation of an oriented matroid. He provides a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations is studied, showing that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. The book finishes by showing examples and a characterization of lifting triangulations.

Full Product Details

Author:   Francisco Santos
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   UK ed.
Volume:   No. 156
Weight:   0.198kg
ISBN:  

9780821827697

ISBN 10:   0821827693
Pages:   80
Publication Date:   28 February 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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