  Using video microscopy, we measure local spatial constraints in disordered
binary colloidal samples, ranging from dilute fluids to jammed glasses, and
probe their spatial and temporal correlations to local dynamics during the
glass transition. We observe the emergence of significant correlations between
constraints and local dynamics within the Lindemann criterion, which coincides
with the onset of glassy dynamics in supercooled liquids. Rigid domains in
fluids are identified based on local constraints, and demonstrate a percolation
transition near glass transition, accompanied by the emergence of dynamical
heterogeneities. Our results show that the spatial constraints instead of the
geometry of amorphous structures is the key that connects the complex
spatial-temporal correlations in disordered materials.
