剪型同余、群同调及示性类SCISSORS CONGRUENCES, GROUP HOMOLOGY & CHARACTERISTIC CLASSES
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作者： Johan L. Dupont著
出 版 社： Penguin
出版时间： 2007-10-26字数：版次： 1页数： 168印刷时间： 2001/02/01开本：印次： 1纸张： 胶版纸I S B N ： 9789810245085包装： 平装内容简介
These lecture notes are based on a series of lectures given at the Narkai 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 byM 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.
目录
Preface
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
Chat)ter 10. Invariants
Chapter 11. Simplices in spherical and hyperbolic 3-space
Chapter 12. Rigidity of Cheeger-Chern-Simons invariants
Chapter 13. Projective configurations and homology of the projective linear group
Chapter 14. Homology of indecomposable configurations
Chapter 15. The case of PGI{3, F)
Appendix A. Spectral sequences and bicomplexes
Bibliography
Index
