  By an integral equation approach to the time-harmonic classical Maxwell
equations, we describe the dispersion in the nonretarded frequency regime of
the edge plasmon-polariton (EPP) on a semi-infinite flat sheet. The sheet has
an arbitrary, physically admissible, tensor valued and spatially homogeneous
conductivity, and serves as a model for a family of two-dimensional conducting
materials. We formulate a system of integral equations for the electric field
tangential to the sheet in a homogeneous and isotropic ambient medium. We show
how this system is simplified via a length scale separation. This view entails
the quasi-electrostatic approximation, by which the tangential electric field
is replaced by the gradient of a scalar potential, $\varphi$. By the
Wiener-Hopf method, we solve an integral equation for $\varphi$ in some
generality. The EPP dispersion relation comes from the elimination of a
divergent limiting Fourier integral for $\varphi$ at the edge. We connect the
existence, or lack thereof, of the EPP dispersion relation to the index for
Wiener-Hopf integral equations, an integer of topological character. We
indicate that the values of this index may express an asymmetry due to the
material anisotropy in the number of wave modes propagating on the sheet away
from the edge with respect to the EPP direction of propagation. We discuss
extensions such as the setting of two semi-infinite, coplanar sheets. Our
theory forms a generalization of the treatment by Volkov and Mikhailov (1988
Sov. Phys. JETP 67 1639).
