  In this Letter we present a detailed study of the lensing configuration in
the cluster Abell 2218. Four multiple-images systems with measured
spectroscopic redshifts have been identified in this cluster. These multiple
images are very useful to constrain accurately the mass distribution in the
cluster core, but they are also sensitive to the value of the geometrical
cosmological parameters of the Universe. Using a simplified maximum likelihood
analysis we find 0 < Omega_M < 0.30 assuming a flat Universe, and 0 < Omega_M <
0.33 and w < -0.85 for a flat Universe with dark energy. Interestingly, an
Einstein-de Sitter model is excluded at more than 4sigma. These constraints are
consistent with the current constraints derived with CMB anisotropies or
supernovae studies. The proposed method constitutes an independent test of the
geometrical cosmological parameters of the Universe and we discuss the limits
of this method and this particular application to Abell 2218. Application of
this method with more sophisticated tools and to a larger number of clusters or
with more multiple images constraints, will put stringent constraints on the
geometrical cosmological parameters.
