Summary ......................................................... v
Acknowledgements .............................................. vii
Introduction .................................................... 1
Chapter 1. Unbounded bivariant K-theory ......................... 5
1. C* -modules .................................................. 5
2. KK-theory ................................................... 12
3. Operator modules ............................................ 17
4. Smoothness .................................................. 22
5. Universal connections ....................................... 28
6. Correspondences ............................................. 37
Chapter 2. Groupoids ........................................... 45
1. A category of groupoids ..................................... 45
2. C*-algebras and -modules .................................... 51
3. Cocycles and if-theory ...................................... 55
4. Crossed products ............................................ 62
5. Semidirect products ......................................... 65
Chapter 3. Limit sets .......................................... 71
1. Limit sets and Patterson-Sullivan measures .................. 71
2. Hyperbolic manifolds ........................................ 75
3. Fuchsian groups ............................................. 81
Bibliography ................................................... 85
Curriculum Vitae ............................................... 87
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