Scissors Congruences, Group Homology And Characteristic Classes

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.

Product details

• Authors: Johan L Dupont, Johan L. Dupont
• Assisted by: Weiping Zhang (Editor)
• Publisher: World Scientific Publishing Company
• Languages: English
• Product format: Hardback
• Released: 01.03.2001
• EAN: 9789810245078
• ISBN: 978-981-02-4507-8
• No. of pages: 176
• Dimensions: 157 mm x 224 mm x 17 mm
• Weight: 390 g
• Series: Nankai Tracts in Mathematics; Nankai Tracts in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra