Scissors Congruences, Group Homology and Characteristic Classes (平裝)

內(nèi)容概要

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 higherdimensions 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.

書籍目錄

PrefaceChapter 1.  Introduction and HistoryChapter 2.  Scissors congruence group and homologyChapter 3.  Homology of flag complexesChapter 4.  Translational scissors congruencesChapter 5.  Euclidean scissors congruencesChapter 6.  Sydler's theorem and non-commutative   differential formsChapter 7.  Spherical scissors congruencesChapter 8.  Hyperbolic scissors congruenceChapter 9.  Homology of Lie groups made discreteChat)ter 10.  InvariantsChapter 11.  Simplices in spherical and hyperbolic 3-spaceChapter 12.  Rigidity of Cheeger-Chern-Simons invariantsChapter 13.  Projective configurations and homology of the   projective linear groupChapter 14.  Homology of indecomposable configurationsChapter 15.  The case of PGI{3, F)Appendix A.  Spectral sequences and bicomplexesBibliographyIndex

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