Discrete Subgroups of Lie Groups

Table of Contents......Page 6
1. Lie Groups and Lie Algebras......Page 7
2. Algebraic Groups......Page 13
3. Group and Lie Algebra Cohomology......Page 18
4. Principal Bundles......Page 20
I. Generalities on Lattices......Page 22
II. Lattices in Nilpotent Lie Groups......Page 35
III. Lattices in Solvable Lie Groups......Page 49
IV. Polycyclic Groups and Arithmeticity of Lattices in Solvable Lie Groups......Page 62
V. Lattices in Semisimple Lie Groups: The Density Theorem of Borel......Page 84
VI. Deformations......Page 95
1. deRham\'s Theorem......Page 111
2. Hodge\'s Theory for Local Systems......Page 114
3. Discrete Subgroups in Lie Groups......Page 117
4. Solvable Lie Groups......Page 121
5. Semisimple Groups (Weil\'s Rigidity Theorem)......Page 129
VIII. Discrete Nilpotent Subgroups of Lie Groups......Page 145
IX. Lattices in Semisimple Lie Groups - A Theorem of Wang......Page 159
X. Arithmetic Groups: Reduction Theory in SL(n) and the Compactness Criterion......Page 165
XI. The Results of Kazdan-Margolis......Page 178
XII. Semisimple Algebraic Groups (Summary of Results)......Page 195
XIII. Fundamental Domains......Page 202
XIV. Existence of Lattices......Page 221
Bibliography......Page 228
Index......Page 233