  We analyze some features of the entanglement entropy for an integer quantum
Hall state ($\nu =1 $) in comparison with ideas from relativistic field theory
and noncommutative geometry. The spectrum of the modular operator, for a
restricted class of states, is shown to be similar to the case of field theory
or a type ${\rm III}_1$ von Neumann algebra. We present arguments that the main
part of the dependence of the entanglement entropy on background fields and
geometric data such as the spin connection is given by a generalized
Chern-Simons form. Implications of this result for bringing together ideas of
noncommutative geometry, entropy and gravity are briefly commented upon.
