  We investigate an index theorem for a Bogoliubov-de Gennes Hamiltonian (BdGH)
describing a topological superconductor with Yang-Mills-Higgs couplings in
arbitrary dimensions. We find that the index of the BdGH is determined solely
by the asymptotic behavior of the Higgs fields and is independent of the gauge
fields. It can be nonvanishing if the dimensionality of the order parameter
space is equal to the spatial dimensions. In the presence of point defects
there appear localized zero energy states at the defects. Consistency of the
index with the existence of zero energy bound states is examined explicitly in
a vortex background in two dimensions and in a monopole background in three
dimensions.
