Lectures on Polytopes
by:
Gunter M. Ziegler
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.
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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).
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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.
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