Lectures on Polytopes

by: Gunter M. Ziegler

Lectures on Polytopes
Author: Gunter M. Ziegler

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Series: Graduate Texts in Mathematics

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Format: Paperback / softback

Publication date: 01 December 1994

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ISBN: 354094365X ISBN 13: 9783540943655

Lectures on Polytopes by Gunter M. Ziegler

Based on a graduate course given at the Technische Universitaet, Berlin, this volume of lecture notes provides an introduction to polytopes. It discusses important examples and constructions, and explores the length and breadth of current research in the field. Top page

Complete description

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present material on the modern theory of convex polytopes. The presentation features 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); and 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). Top page

General info

Publisher & Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

City: Berlin

Pages: 379

More info: height 216 mm width 138 mm weight 535 gr

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Age recommended: College/higher education

Subject Indexing & Classification Dewey:(DC20) 516.35

Departments: Algebraic geometry; Topology;

Record updated at: 25 May, 2012 time: 02:57

Summary Lectures on Polytopes Preface.- Preface to the Second Printing.- 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, Anrrangements, Zonotopes, and Tilings.- Shellability and the Upper Bound Theorem. Fiber Polytopes, and Beyond.- References.- Index. Top page

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