Geometrical Description of the Fractional Quantum Hall Effect
  The fundamental collective degree of freedom of fractional quantum Hall states is identified as a unimodular two-dimensional spatial metric that characterizes the local shape of the correlations of the incompressible fluid. Its quantum fluctuations are controlled by a topologically-quantized "guiding-center spin". Charge fluctuations are proportional to its Gaussian curvature. 
F. D. M. Haldane
cond-mat.mes-hall gr-qc hep-th