These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert’s Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.
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Lingua Inglese ● Formato PDF ● Pagine 176 ● ISBN 9789812810335 ● Dimensione 5.4 MB ● Casa editrice World Scientific Publishing Company ● Città Singapore ● Paese SG ● Pubblicato 2001 ● Scaricabile 24 mesi ● Moneta EUR ● ID 2447089 ● Protezione dalla copia Adobe DRM
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