03325nam 2200637Ia 450 991045440130332120200520144314.01-281-95184-69786611951849981-281-033-1(CKB)1000000000538069(EBL)1679403(SSID)ssj0000242419(PQKBManifestationID)11215422(PQKBTitleCode)TC0000242419(PQKBWorkID)10310782(PQKB)11467164(MiAaPQ)EBC1679403(WSP)00004598(Au-PeEL)EBL1679403(CaPaEBR)ebr10255746(OCoLC)815754738(EXLCZ)99100000000053806920010703d2001 uy 0engur|n|---|||||txtccrScissors congruences, group homology and characteristic classes[electronic resource] /Johan L. DupontSingapore ;River Edge, NJ World Scientificc20011 online resource (178 p.)Nankai tracts in mathematics ;1Description based upon print version of record.981-02-4507-6 Includes bibliographical references (p. 159-165) and index.Preface; Contents; Chapter 1. Introduction and History; Chapter 2. Scissors congruence group and homology; Chapter 3. Homology of flag complexes; Chapter 4. Translational scissors congruences; Chapter 5. Euclidean scissors congruences; Chapter 6. Sydler's theorem and non-commutative differential forms; Chapter 7. Spherical scissors congruences; Chapter 8. Hyperbolic scissors congruence; Chapter 9. Homology of Lie groups made discrete; Chapter 10. Invariants; Chapter 11. Simplices in spherical and hyperbolic 3-space; Chapter 12. Rigidity of Cheeger-Chern-Simons invariantsChapter 13. Projective configurations and homology of the projective linear groupChapter 14. Homology of indecomposable configurations; Chapter 15. The case of PGl(3,F); Appendix A. Spectral sequences and bicomplexes; Bibliography; IndexThese 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 grNankai tracts in mathematics ;v. 1.TetrahedraVolume (Cubic content)Characteristic classesElectronic books.Tetrahedra.Volume (Cubic content)Characteristic classes.516.23Dupont Johan L55031MiAaPQMiAaPQMiAaPQBOOK9910454401303321Scissors congruences, group homology and characteristic classes2255458UNINA