  By obtaining photometric redshift information, tomography allows us to
cross-correlate galaxy ellipticities in different source redshift bins. The
cross-correlation is non-vanishing because the different bins share much of the
foreground mass distribution from which, over Gpc scales, the lensing signal is
built. If the redshift bins are thick enough however, the cross-correlations
are insensitive to contamination from the intrinsic alignments of galaxies
since these fall off rapidly on scales larger than a few tens of Mpc. We
forecast how lensing tomography using only the cross-power spectra can
constrain cosmological parameters compared to tomography including the
auto-spectra. It is shown that the parameter errors are degraded by only O(10%)
for 5 or more source redshift bins. Thus, the cross-power spectrum tomography
can be a simple, model-independent means of reducing the intrinsic alignment
contamination while retaining most of the constraints on cosmology.
