  IceTop is an air shower array located on the Antarctic ice sheet at the
geographic South Pole. IceTop can detect an astrophysical flux of neutrons from
Galactic sources as an excess of cosmic ray air showers arriving from the
source direction. Neutrons are undeflected by the Galactic magnetic field and
can typically travel 10 ($E$ / PeV) pc before decay. Two searches are performed
using 4 years of the IceTop dataset to look for a statistically significant
excess of events with energies above 10 PeV ($10^{16}$ eV) arriving within a
small solid angle. The all-sky search method covers from -90$^{\circ}$ to
approximately -50$^{\circ}$ in declination. No significant excess is found. A
targeted search is also performed, looking for significant correlation with
candidate sources in different target sets. This search uses a higher energy
cut (100 PeV) since most target objects lie beyond 1 kpc. The target sets
include pulsars with confirmed TeV energy photon fluxes and high-mass X-ray
binaries. No significant correlation is found for any target set. Flux upper
limits are determined for both searches, which can constrain Galactic neutron
sources and production scenarios.
