  Despite our present-day inability to predict the topology of the universe one
may expect that we should be able to detect it in the near future, given the
increasing accuracy in the astro-cosmological observations. Motivated by this,
we examine to what extent a possible detection of a non-trivial topology of a
low curvature (Omega_0 ~ 1) universe, suggested by a diverse set of current
observations, may be used to place constraints on the matter content of the
universe, focusing our attention on the generalized Chaplgygin gas (GCG) model,
which unifies dark matter and dark energy in a single matter component. We show
that besides constraining the GCG free parameters, the detection of a
nontrivial topology also allows to set bounds on the total density parameter
Omega_0. We also study the combination of the bounds from the topology
detection with the limits that arise from current data on 194 SNIa, and show
that the determination of a given nontrivial topology sets complementary bounds
on the GCG parameters (and on Omega_0) to those obtained from the SNIa data.
