| 1 |
Introduction |
1 |
| 2 |
Noncommutative Spaces and
Algebras of Functions |
7 |
| 3 |
Projective Systems of
Noncommutative Lattices |
21 |
| 4 |
Modules as Bundles |
59 |
| 5 |
A Few Elements of K-Theory |
69 |
| 6 |
The Spectral Calculus |
83 |
| 7 |
Noncommutative Differential
Forms |
105 |
| 8 |
Connections on Modules |
121 |
| 9 |
Field Theories on Modules |
131 |
| 10 |
Gravity Models |
149 |
| 11 |
Quantum Mechanical Models on
Noncommutative Lattices |
163 |
|
A. Appendices |
167 |
| A.1 |
Basic Notions of Topology |
167 |
| A.2 |
The Gelfand-Naimark-Segal
Construction |
170 |
| A.3 |
Hilbert Modules |
173 |
| A.4 |
Strong Morita Equivalence |
179 |
| A.5 |
Partially Ordered Sets |
182 |
| A.6 |
Pseudodifferential Operators |
184 |
|
References |
189 |
|
Index |
197 |