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Basics of Noncommutative Geometry

Course Type: 
PhD Course
Academic Year: 
2013-2014
Period: 
October-November
Duration: 
20 h
Description: 
  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: De finition. The trace property. Computations for the examples. Gauss-Bonnet for the noncommutative two torus.
  3. Index Theory.
    • The Index of Fredholm operators: Properties: additivity and homotopy invariance. Explicit computations for the case of S1: the winding number.
Lecture notes.
Location: 
A-136

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