  Glass-forming liquids are broadly classified as being fragile or strong,
depending on the deviation from Arrhenius behavior of their relaxation times. A
fragile to strong crossover is observed or inferred in liquids like water and
silica, and more recently also in metallic glasses and phase change alloys,
leading to the expectation that such a crossover is more widely realised among
glass formers. We investigate computationally the well-studied Kob-Andersen
model, accessing temperatures well below the mode coupling temperature
$T_{MCT}$. We find that relaxation times exhibit a crossover in dynamics around
$T_{MCT}$, and discuss whether it bears characteristics of the fragile to
strong crossover. Several aspects of dynamical heterogeneity exhibit behavior
mirroring the dynamical crossover, whereas thermodynamic quantities do not. In
particular, the Adam-Gibbs relation describing the relation between relaxation
times and configurational entropy continues to hold below the dynamical
crossover, when anharmonic corrections to the vibrational entropy are included.
