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Quantum Groups and Noncommutative Geometry

Basics of Noncommutative Geometry

  1. Noncommutative Topology.
    • Motivation. The dictionary.
  2. Noncommutative Geometry.
    • Spectral Triples: The data set. The compact resolvent condition. Boundedness of the commutators. Examples of spectral triples: the circle S1; the noncommutative torus.
    • Spectral Dimension and the zeta function: Definition. The trace property. Computations for the examples. Gauss-Bonnet for the noncommutative two torus.


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