Fredholm Indices and the Phase Diagram of Quantum Hall Systems
  The quantized Hall conductance in a plateau is related to the index of a Fredholm operator. In this paper we describe the generic ``phase diagram'' of Fredholm indices associated with bounded and Toeplitz operators. We discuss the possible relevance of our results to the phase diagram of disordered integer quantum Hall systems. 
Joseph E. Avron and Lorenzo Sadun