Topological states of matter and noncommutative geometry
This thesis examines topological states of matter from the perspective of noncommutative geometry and KK-theory. Examples of such topological states of matter include the quantum Hall e ect and topological insulators. For the quantum Hall e ect, we consider a continuous model and show that the Hall conductance can be expressed in terms of the index pairing of the Fermi projection of a disordered Hamiltonian with a spectral triple encoding the geometry of the sample's momentum space. The...[Show more]
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