1.

Record Nr.

UNINA9910454401303321

Autore

Dupont Johan L

Titolo

Scissors congruences, group homology and characteristic classes [[electronic resource] /] / Johan L. Dupont

Pubbl/distr/stampa

Singapore ; ; River Edge, NJ, : World Scientific, c2001

ISBN

1-281-95184-6

9786611951849

981-281-033-1

Descrizione fisica

1 online resource (178 p.)

Collana

Nankai tracts in mathematics ; ; 1

Disciplina

516.23

Soggetti

Tetrahedra

Volume (Cubic content)

Characteristic classes

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. 159-165) and index.

Nota di contenuto

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

Sommario/riassunto

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