Minkowski Functionals of Convergence Maps and the Lensing Figure of
  Merit
  Minkowski functionals (MFs) quantify the topological properties of a given
field probing its departure from Gaussianity. We investigate their use on
lensing convergence maps in order to see whether they can provide further
insights on the underlying cosmology with respect to the standard second-order
statistics, i.e., cosmic shear tomography. To this end, we first present a
method to match theoretical predictions with measured MFs taking care of the
shape noise, imperfections in the map reconstruction, and inaccurate
description of the nonlinearities in the matter power spectrum and bispectrum.
We validate this method against simulated maps reconstructed from shear fields
generated by the MICE simulation. We then perform a Fisher matrix analysis to
forecast the accuracy on cosmological parameters from a joint MFs and shear
tomography analysis. It turns out that MFs are indeed helpful to break the
$\Omega_{\rm m}$--$\sigma_8$ degeneracy thus generating a sort of chain
reaction leading to an overall increase of the Figure of Merit.
