  We present a theoretical and exact analysis of the bispectrum of projected
galaxy catalogues. The result can be generalized to evaluate the projection in
spherical harmonics of any 3D bispectrum and therefore has applications to
cosmic microwave background and gravitational lensing studies. By expanding the
2D distribution of galaxies on the sky in spherical harmonics, we show how the
3-point function of the coefficients can be used in principle to determine the
bias parameter of the galaxy sample. If this can be achieved, it would allow a
lifting of the degeneracy between the bias and the matter density parameter of
the Universe which occurs in linear analysis of 3D galaxy catalogues. In
previous papers we have shown how a similar analysis can be done in three
dimensions, and we show here, through an error analysis and by implementing the
method on a simulated projected catalogue, that ongoing three-dimensional
galaxy redshift surveys (even with all the additional uncertainties introduced
by partial sky coverage, redshift-space distortions and smaller numbers) will
do far better than all-sky projected catalogues with similar selection
function.
