  Fast-slow dynamical systems have subsystems that evolve on vastly different
timescales, and bifurcations in such systems can arise due to changes in any or
all subsystems. We classify bifurcations of the critical set (the equilibria of
the fast subsystem) and associated fast dynamics, parametrized by the slow
variables. Using a distinguished parameter approach we are able to classify
bifurcations for one fast and one slow variable. Some of these bifurcations are
associated with the critical set losing manifold structure. We also conjecture
a list of generic bifurcations of the critical set for one fast and two slow
variables. We further consider how the bifurcations of the critical set can be
associated with generic bifurcations of attracting relaxation oscillations
under an appropriate singular notion of equivalence.
