  Harnessing a model from composite materials science, we show how point-like
cusped surface features arise as quasi-particle excitations, termed "ghost
fibers", on the surface of a homogeneous soft elastic material. These
deformations appear above a critical compressive strain at which ghost fiber
dipoles unbind, analogous to vortices in the Kosterlitz-Thouless transition.
Finite-length creases can be described in the same framework. Our predictions
for crease surface profiles and onset strain agree with previous experiments
and simulations, and further experimental tests are proposed.
