## Elements of Noncommutative Geometry

### Prof. Ludwik Dabrowski

Prerequisites: the lecture courses of Piacitelli and Bruzzo

Contents:

- Vector bundles as projective finitely generated modules
- Projectors and K-theory
- Hermitean structure as Hilbert modules; Morita equivalence
- Connections, covariant derivatives, curvature, Chern character, Chern-Weyl homomorphism on deRham homology
- Derivation-based calculus, Hochshild cyclic homology, cycles on A, Fredholm modules
- Noncommutative integral, metric spin structure (spectral triples)
- Examples: the noncommutative torus, SLq(2), Sq2