  Local topological markers have proven to be a valuable tool for investigating
systems with topologically non-trivial bands. Due to their local nature, such
markers can treat translationally invariant systems and spatially inhomogeneous
systems on an equal footing. Among the most prevalent of these is the so-called
Chern marker, which is available for systems in two spatial dimensions. In this
paper, we describe how to generalize this marker to 1d and 3d systems, by
showing that the relevant expressions accurately describe the phenomenon of
topological pumping given by the first and second Chern numbers in 1d and 3d
respectively. In addition to providing general derivations, we verify the
markers by numerically considering model Hamiltonians. These results will open
the door for future studies including the influence of disorder on topological
pumping and topological phase transitions in odd-dimensional systems.
