We numerically study the interplay between heterogeneous dynamics and
properties of negatively curved regions of the potential energy surface in a
model glassy system. We find that the unstable modes of saddles and
quasi-saddles undergo a localization transition close to the Mode-Coupling
critical temperature. We also find evidence of a positive spatial correlation
between clusters of particles having large displacements in the unstable modes
and dynamical heterogeneities.Comment: 7 pages, 3 figures, submitted to Europhys. Let
