  Kinetically constrained models (KCMs) are models of glass formers based on
the concept of dynamic facilitation. This concept accounts for many of the
characteristics of the glass transition. KCMs usually display a combination of
simple thermodynamics and complex glassy dynamics, the latter being a
consequence of kinetic constraints. Here we show that KCMs can be regarded as
systems whose configuration space is endowed with a simple energy surface but a
complicated geometry. This geometry is determined solely by the kinetic
constraints, and determines the dynamics of the system. It does not affect the
overall distribution of states. Low temperature dynamical slow-down is then a
consequence of the competition between the paths allowed by the geometry of
configuration space, and those leading to energy relaxation. This competition
gives rise to dynamical bottlenecks unrelated to static properties. This view
of the dynamics is distinct from that based on an underlying static rugged
energy landscape. We illustrate our ideas with simple examples.
