  A theory of sections of simplicial height functions is developed. At the core
of this theory lies the section complex, which is assembled from higher section
spaces. The latter encode flow lines along the height, as well as their
homotopies, in a combinatorial way. The section complex has an associated
spectral sequence, which computes the homology of the height functions domain.
We extract Reeb complexes from the spectral sequence. These provide a first
order approximation of how homology generators flow along height levels. Our
theory in particular models topological section spaces of piecewise linear
functions in a completely combinatorial way.
