Scissors Congruences, Group Homology and Characteristic Classes

By Johan L. Dupont

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.

• Format: Paperback
• Language: English
• ISBN: 9810245084
• ISBN13: 9789810245085
• Release Date: February 2001
• Publisher: World Scientific Publishing Company
• Length: 176 Pages
• Weight: 0.54 lbs.
• Dimensions: 0.4" x 6.0" x 8.5"