  We introduce topological methods for quantifying spatially heterogeneous
dynamics, and use these tools to analyze particle-tracking data for a
quasi-two-dimensional granular system of air-fluidized beads on approach to
jamming. In particular we define two overlap order parameters, which quantify
the correlation between particle configurations at different times, based on a
Voronoi construction and the persistence in the resulting cells and nearest
neighbors. Temporal fluctuations in the decay of the persistent area and bond
order parameters define two alternative dynamic four-point susceptibilities,
XA(t) and XB(t), well-suited for characterizing spatially-heterogeneous
dynamics. These are analogous to the standard four-point dynamic susceptibility
X4(l,t), but where the space-dependence is fixed uniquely by topology rather
than by discretionary choice of cutoff function. While these three
susceptibilities yield characteristic time scales that are somewhat different,
they give domain sizes for the dynamical heterogeneities that are in good
agreement and that diverge on approach to jamming.
