  The topological terms of the bulk effective action for the integer quantum
Hall effect, capturing the dynamics of gauge and gravitational fluctuations,
reveal a curiosity, namely, the Abelian potential for the magnetic field
appears in a particular combination with the Abelian spin connection. This
seems to hold for quantum Hall effect on complex projective spaces of arbitrary
dimensions. An interpretation of this in terms of the algebra of symplectic
transformations is given. This can also be viewed in terms of the metaplectic
correction in geometric quantization.
