  We illustrate the constraints that a possible detection of a non-trivial
spatial topology may place on the cosmological density parameters by
considering the $\Lambda$CDM model Poincar\'e dodecahedal space (PDS) topology
as a circles-in-the-sky detectable topology. To this end we reanalyze the type
Ia supernovae constraints on the density parameter plane
$\Omega_k$--$\Omega_{\Lambda}$ and show that a circles-in-the-sky detectable
PDS topology gives rise to important constraints on this parameters plane.
