  Re-configurable materials and meta-materials can jump between space symmetry
classes during their deformations. Here, we introduce the concept of singular
symmetry enhancement, which refers to an abrupt jump to a higher symmetry class
accompanied by an un-avoidable reduction in the number of dispersion bands of
the excitations of the material. Such phenomenon prompts closings of some of
the spectral resonant gaps along singular manifolds in a parameter space. In
this work, we demonstrate that these singular manifolds can carry topological
charges. As a concrete example, we show that a deformation of an acoustic
crystal that encircles a p11g-symmetric configuration of an array of cavity
resonators results in an adiabatic cycle that carries a Chern number in the
bulk and displays Thouless pumping at the edges. This points to a very general
guiding principle for recognizing cyclic adiabatic processes with high
potential for topological pumping in complex materials and meta-materials,
which rests entirely on symmetry arguments.
