  Three-point weak lensing statistics provide cosmic information complementary
to that of two-point statistics. However, both statistics suffer from
intrinsic-shear alignment, which is one of their limiting systematics. The
nulling technique is a model-independent method developed to eliminate
intrinsic-shear alignment at the two-point level. In this paper we demonstrate
that the nulling technique can also be naturally generalized to the three-point
level, controlling the corresponding GGI systematics. We show that under the
assumption of exact redshift information the intrinsic-shear alignment
contamination can be completely eliminated. To show how well the nulling
technique performs on data with limited redshift information, we apply the
nulling technique to three-point weak lensing statistics from a fictitious
survey analogous to a typical future deep imaging survey, in which the
three-point intrinsic-shear alignment systematics is generated from a power-law
toy model. Using 10 redshift bins, the nulling technique leads to a factor of
10 suppression of the GGI/GGG ratio, and reduces the bias on cosmological
parameters to less than the original statistical error. More detailed redshift
information allowing for finer redshift bins leads to better reduction of bias.
The information loss during the nulling procedure doubles the statistical error
on cosmological parameters. A comparison of the nulling technique with an
unconditioned compression of the data suggests that part of the information
loss can be retained by considering higher-order nulling weights during the
nulling procedure. A combined analysis of two- and three-point statistics
confirms that the information contained in them is of comparable size and is
complementary to each other, both before and after nulling.
