Elements of Noncommutative Geometry

Prof. Ludwik Dabrowski

Prerequisites: the lecture courses of Piacitelli and Bruzzo


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