Triangulations of Oriented Matroids

Buch | Softcover

2002
American Mathematical Society (Verlag)
978-0-8218-2769-7 (ISBN)

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Considers the concept of triangulation of an oriented matroid. This book studies the relation existing between triangulations of an oriented matroid $/mathcal{M}$ and extensions of its dual $/mathcal{M}^*$, via the so-called lifting triangulations.

We consider the concept of triangulation of an oriented matroid. We provide 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 we study the relation existing between triangulations of an oriented matroid $/mathcal{M}$ and extensions of its dual $/mathcal{M}^*$, via the so-called lifting triangulations. We show 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. We finish by showing examples and a characterization of lifting triangulations.

Introduction Preliminaries on oriented matroids Triangulations of oriented matroids Duality between triangulations and extensions Subdivisions of Lawrence polytopes Lifting triangulations Bibliography.

Erscheint lt. Verlag	28.2.2002
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	bibliography
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-2769-3 / 0821827693
ISBN-13	978-0-8218-2769-7 / 9780821827697
Zustand	Neuware