  Motivated by the geometric character of spin Hall conductance, the
topological invariants of generic superconductivity are discussed based on the
Bogoliuvov-de Gennes equation on lattices.
  They are given by the Chern numbers of degenerate condensate bands for
unitary order, which are realizations of Abelian chiral anomalies for
non-Abelian connections. The three types of Chern numbers for the $x,y$ and
$z$-directions are given by covering degrees of some doubled surfaces around
the Dirac monopoles. For nonunitary states, several topological invariants are
defined by analyzing the so-called $q$-helicity. Topological origins of the
nodal structures of superconducting gaps are also discussed.
