UID:
almafu_9959228635402883
Format:
1 online resource (178 p.)
Edition:
1st ed.
ISBN:
1-281-95184-6
,
9786611951849
,
981-281-033-1
Series Statement:
Nankai tracts in mathematics ; 1
Content:
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 gr
Note:
Description based upon print version of record.
,
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
,
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
,
English
Additional Edition:
ISBN 981-02-4507-6
Language:
English
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