| Description |
1 online resource (viii, 168 pages) : illustrations |
| Series |
Nankai tracts in mathematics ; 1 |
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Nankai tracts in mathematics ; v. 1.
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| Contents |
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 invariants |
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Chapter 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; Index |
| Summary |
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", ie. 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, characteristics 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 |
| Bibliography |
Includes bibliographical references (pages 159-165) and index |
| Notes |
Print version record |
| Subject |
Tetrahedra.
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Volume (Cubic content)
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Characteristic classes.
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tetrahedra.
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volumes (documents by form)
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volume (quantity or mass)
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MATHEMATICS -- Measurement.
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Characteristic classes
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Tetrahedra
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Volume (Cubic content)
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| Form |
Electronic book
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| ISBN |
9789812810335 |
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9812810331 |
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1281951846 |
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9781281951847 |
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9789810245085 |
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9810245084 |
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