  We define a class of multiparameter persistence modules that arise from a
one-parameter family of functions on a topological space and prove that these
persistence modules are stable. We show that this construction can produce
indecomposable persistence modules with arbitrarily large dimension. In the
case of smooth functions on a compact manifold, we apply cobordism theory and
Cerf theory to study the resulting persistence modules. We give examples in
which we obtain a complete description of the persistence module as a direct
sum of indecomposable summands and provide a corresponding visualization.
