Lectures on Polytopes

Gunter M. Ziegler - Collection Graduate Texts in Mathematics

388 pages, parution le 31/01/1998

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Résumé

Based on a graduate course given at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions.

The lectures

introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids)
discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction)
show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) They should provide interesting and enjoyable reading for researchers as well as students.

Written for: Graduate students of Math

L'auteur - Gunter M. Ziegler

Technische Universität Berlin, Germany.

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Sommaire

Introduction and Examples
Polytopes, Polyhedra, and Cones
Faces of Polytopes
Graphs for Polytopes
Steinitz' Theorem for 3-Polytopes
Schlegel Diagrams for 4-Polytopes
Duality, Gale Diagrams, and Applications
Fans, Arrangements, Zonotopes, and Tilings
Shellability and the Upper Bound Theorem
Fiber Polytopes, and Beyond

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Gunter M. Ziegler
Collection	Graduate Texts in Mathematics
Parution	31/01/1998
Nb. de pages	388
Format	15,5 x 23,5
Couverture	Broché
Poids	560g
Intérieur	Noir et Blanc
EAN13	9780387943657
ISBN13	978-0-387-94365-7