[L2] _________________________ AMAST Links 01 03

Lectures on Polytopes Available

I am happy to announce that my ``Lectures on Polytopes'' finally do exist in print, and want to thank everyone for all the support I received with this project.

Günter M. Ziegler
ziegler@math.tu-berlin.de
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Günter M. Ziegler: ``Lectures on Polytopes''
Graduate Texts in Mathematics 152,
Springer-Verlag New York Berlin Heidelberg 1995, 370 pages.
Europe: hardcover DM 108,00 ISBN 3-540-94329-3 softcover DM 48,00 ISBN 3-540-94365-X
US: hardcover $ 59.00 ISBN 0-387-94329-3 softcover $ 29.00 ISBN 0-387-94365-X
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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 diagrams, oriented matroids)
• discuss important examples and elegant constructions (cyclic and neighbourly 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, nonextendable shellings)