  Two fundamental questions regarding our description of the Universe concern
the geometry and topology of its 3-dimensional space. While geometry is a local
characteristic that gives the intrinsic curvature, topology is a global feature
that characterizes the shape and size of the 3-space. The geometry constrains,
but does not dictate the the spatial topology. We show that, besides
determining the spatial geometry, the knowledge of the spatial topology allows
to place tight constraints on the density parameters associated with dark
matter ($\Omega_m$) and dark energy ($\Omega_{\Lambda}$). By using the
Poincar\'e dodecahedral space as the observable spatial topology, we reanalyze
the current type Ia supenovae (SNe Ia) constraints on the density parametric
space $\Omega_{m} - \Omega_{\Lambda}$. From this SNe Ia plus cosmic topology
analysis, we found best fit values for the density parameters, which are in
agreement with a number of independent cosmological observations.
