  With the recent launch of the Hinode satellite our view of the nature and
evolution of quiet-Sun regions has been improved. In light of the new high
resolution observations, we revisit the study of the quiet Sun's topological
nature. Topology is a tool to explain the complexity of the magnetic field, the
occurrence of reconnection processes, and the heating of the corona. This
Letter aims to give new insights to these different topics. Using a
high-resolution Hinode/SOT observation of the line-of-sight magnetic field on
the photosphere, we calculate the three dimensional magnetic field in the
region above assuming a potential field. From the 3D field, we determine the
existence of null points in the magnetic configuration. From this model of a
continuous field, we find that the distribution of null points with height is
significantly different from that reported in previous studies. In particular,
the null points are mainly located above the bottom boundary layer in the
photosphere (54%) and in the chromosphere (44%) with only a few null points in
the corona (2%). The density of null points (expressed as the ratio of the
number of null points to the number of photospheric magnetic fragments) in the
solar atmosphere is estimated to be between 3% and 8% depending on the method
used to identify the number of magnetic fragments in the observed photosphere.
This study reveals that the heating of the corona by magnetic reconnection at
coronal null points is unlikely. Our findings do not rule out the heating of
the corona at other topological features. We also report the topological
complexity of the chromosphere as strongly suggested by recent observations
from Hinode/SOT.
