  An effective action for the bulk dynamics of quantum Hall effect in arbitrary
even spatial dimensions was obtained some time ago in terms of a Chern-Simons
term associated with the Dolbeault index theorem. Here we explore further
properties of this action, showing how electronic band structures can be
incorporated, obtaining Hall currents and conductivity (for arbitrary
dimensions) in terms of integrals of Chern classes for the bands. We also
derive the expression for Hall viscosity from the effective action. Explicit
formulae for the Hall viscosity are given for 2+1 and 4+1dimensions.
