  Inelastic neutron scattering was used to study the low-lying nuclear
structure of $^{132}$Xe. A comprehensive level scheme is presented, as well as
new level lifetimes, multipole mixing ratios, branching ratios, and transition
probabilities. Comparisons of these data as well as previously measured $E2$
strengths and $g$ factors are made with new shell-model calculations for
$^{132,134,136}$Xe to explore the emergence of collectivity in the Xe isotopes
with $N$ < 82 near the closed shell.
