  We propose a new scenario for glassy dynamics in frustrated systems with no
quenched-in randomness, based on jamming of extended dynamical structures near
a critical point. This route to a glassy state is demonstrated in a lattice
model of fluctuating lines. Numerical simulations of the model show
non-exponential relaxations and diverging energy barriers in the vicinity of a
thermodynamic phase transition. A master equation for the coarse grained
dynamics is constructed. It shows how topological jamming leads to the observed
glassy dynamics.
