  Topological insulators are new phases of matter whose properties are derived
from a number of qualitative yet robust topological invariants rather than
specific geometric features or constitutive parameters. Here, Kagome lattices
are classified based on a topological invariant directly related to the
handedness of a couple of elliptically polarized stationary eigenmodes in the
context of what is known as the "quantum valley Hall effect" in physics
literature. An interface separating two topologically distinct lattices, i.e.,
two lattices with different topological invariants, is then proven to host two
topological Stoneley waves whose frequencies, shapes and decay and propagation
velocities are quantified. Conversely, an interface separating two
topologically equivalent lattices will host no Stoneley waves. Analysis is
based on an asymptotic model derived through a modified high-frequency
homogenization procedure. This case study constitutes the first implementation
of the quantum valley Hall effect in in-plane elasticity. A preliminary
discussion of 1D lattices is included to provide relevant background on
topological effects in a simple analytical framework.
