  Research on high-$T_c$ superconductors has generally not focused on analysis
of the topological structure of electronic bands in these materials. In this
article we collate and discuss several well-known experimental observables that
signal that certain signatures of topology may be present. The topological
signatures suggested by experiment include dimensional reduction, electronic
transport determined by loop statistics, a winding number, Weyl fermions, and
others. We suggest that topology, in a wider sense than band topology, may be
key to the mechanism of high-$T_c$ superconductivity.
