Oriented Matroids
Seiten
2025
Cambridge University Press (Verlag)
978-1-009-49411-3 (ISBN)
Cambridge University Press (Verlag)
978-1-009-49411-3 (ISBN)
Oriented matroids appear throughout discrete geometry and have applications in algebra, topology, physics, and data analysis. This introductory text is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. No knowledge of matroid theory is assumed.
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.
Laura Anderson is Associate Professor in the Department of Mathematics and Statistics at Binghamton University. Her research focuses on interactions between combinatorics and topology, particularly those involving oriented matroids, convex polytopes, and other concepts from discrete geometry.
1. Realizable oriented matroids; 2. Oriented matroids; 3. Elementary operations and properties; 4. The topological representation theorem; 5. Strong maps and weak maps; 6. Single-element extensions; 7. The universality theorem; 8. Oriented matroid polytopes; 9. Subdivisions and triangulations; 10. Spaces of oriented matroids; 11. Hints on selected exercises; References; Index.
| Erscheinungsdatum | 14.05.2025 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-009-49411-2 / 1009494112 |
| ISBN-13 | 978-1-009-49411-3 / 9781009494113 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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