Progress in Mathematics

By: Ernst Kleinert

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Hardcover | 1 April 2000

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92 Pages

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24.13 x 15.88 x 0.64

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0 Basic Facts.- 1 Hey's Theorem and Consequences.- 2 Siegel-Weyl Reduction Theory.- 3 The Tamagawa Number and the Volume of G(?)/G(?).- 3.1 Statement of the main result.- 3.2 Proof of 3.1.- 3.3 The volume of G(?)/G(?).- 4 The Size of ?.- 4.1 Statement of results.- 4.2 Proofs.- 5 Margulis' Finiteness Theorem.- 5.1 The Result.- 5.2 Amenable groups.- 5.3 Kazhdan's property (T).- 5.4 Proof of 5.1; beginning.- 5.5 Interlude: parabolics and their opposites.- 5.6 Continuation of the proof.- 5.7 Contracting automorphisms and the Moore Ergodicity theorem.- 5.8 End of proof.- 5.9 Appendix on measure theory.- 6 A Zariski Dense and a Free Subgroup of ?.- 7 An Example.- 8 Problems.- 8.1 Generators.- 8.2 The congruence problem.- 8.3 Betti numbers.- References.

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Introduction and Survey of Results
Basic Facts	p. 1
Hey's Theorem and Consequences	p. 5
Siegel-Weyl Reduction Theory	p. 8
The Tamagawa Number and the Volume of G(R)/G(Z)	p. 17
The Size of [Gamma]	p. 31
Margulis' Finiteness Theorem	p. 41
A Zariski Dense and a Free Subgroup of [Gamma]	p. 60
An Example	p. 66
Problems	p. 72
References	p. 77
Index	p. 80
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

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