When the topology of the universe is non-trivial, there exist constrai
nts on the network of topological defects that may appear during a pha
se transition in the early universe. Here we review the main results o
f two recent papers by Uzan and Peter concerning topological defects i
n a multiconnected universe: the no-defect conjecture, the evaluation
of the redshift at which all the defects (if formed) have disappeared
and the consequence on the cosmic microwave background.