  Canonical quantum gravity provides insights into the quantum dynamics as well
as quantum geometry of space-time by its implications for constraints. Loop
quantum gravity in particular requires specific corrections due to its
quantization procedure, which also results in a discrete picture of space. The
corresponding changes compared to the classical behavior can most easily be
analyzed in isotropic models, but perturbations around them are more involved.
For one type of corrections, consistent equations have been found which shed
light on the underlying space-time structure at the Planck scale: not just
quantum dynamics but also the concept of space-time manifolds changes in
quantum gravity. Effective line elements provide indications for possible
relationships to other frameworks, such as non-commutative geometry.
