  Topology has appeared in different physical contexts. The most prominent
application is topologically protected edge transport in condensed matter
physics. The Chern number, the topological invariant of gapped Bloch
Hamiltonians, is an important quantity in this field. Another example of
topology, in polarization physics, are polarization singularities, called L
lines and C points. By establishing a connection between these two theories, we
develop a novel technique to visualize and potentially measure the Chern
number: it can be expressed either as the winding of the polarization azimuth
along L lines in reciprocal space, or in terms of the handedness and the index
of the C points. For mechanical systems, this is directly connected to the
visible motion patterns.
