  The $\beta$-decay half-lives of 55 neutron-rich nuclei $^{134-139}$Sn,
$^{134-142}$Sb, $^{137-144}$Te, $^{140-146}$I, $^{142-148}$Xe, $^{145-151}$Cs,
$^{148-153}$Ba, $^{151-155}$La were measured at the Radioactive Isotope Beam
Factory (RIBF) employing the projectile fission fragments of $^{238}$U. The
nuclear level structure, which relates to deformation, has a large effect on
the half-lives. The impact of newly-measured half-lives on modeling the
astrophysical origin of the heavy elements is studied in the context of $r$
process nucleosynthesis. For a wide variety of astrophysical conditions,
including those in which fission recycling occurs, the half-lives have an
important local impact on the second ($A$ $\approx$ 130) peak.
