Title: Note on Green Function Formalism and Topological Invariants,
Abstract: It has been discovered previously that the topological order parameter could
be identified from the topological data of the Green function, namely the
(generalized) TKNN invariant in general dimensions, for both non-interacting
and interacting systems. In this note, we show that this phenomena has a clear
geometric derivation. This proposal could be regarded as an alternative proof
for the identification of the corresponding topological invariant and
topological order parameter.