  In recent years there has been a great interest in topological materials and
in their fascinating properties. Topological band theory was initially
developed for condensed matter systems, but it can be readily applied to
arbitrary wave platforms with little modifications. Thus, the topological
classification of optical systems is usually regarded as being mathematically
equivalent to that of condensed matter systems. Surprisingly, here we find that
both the particle-hole symmetry and the dispersive nature of nonreciprocal
photonic materials may lead to situations where the usual topological methods
break-down and the Chern topology becomes ill-defined. It is shown that due to
the divergence of the density of photonic states in plasmonic systems the gap
Chern numbers can be non-integer notwithstanding that the relevant parametric
space is compact. In order that the topology of a dispersive photonic crystal
is well defined, it is essential to take into account the nonlocal effects in
the bulk-materials. We propose two different regularization methods to fix the
encountered problems. Our results highlight that the regularized topologies may
depend critically on the response of the bulk materials for large k.
