  Given an algebraic structure on the homology of a chain complex, we define
its realization space as a Kan complex whose vertices are the structures up to
homotopy realizing this structure at the homology level. Our algebraic
structures are parametrised by props and thus include various kinds of
bialgebras. We give a general formula to compute subsets of equivalences
classes of realizations as quotients of automorphism groups, and determine the
higher homotopy groups via the cohomology of deformation complexes. As a
motivating example, we compute subsets of equivalences classes of realizations
of Poincar\'e duality for several examples of manifolds.
