  We consider the moduli spaces $\mathcal{M}_d(\ell)$ of a closed linkage with
n links and prescribed lengths in d-dimensional Euclidean space. For d>3 these
spaces are no longer manifolds generically, but they have the structure of a
pseudomanifold. We use intersection homology to assign a ring to these spaces
that can be used to distinguish the homeomorphism type of the moduli spaces for
a large class of length vectors in the case of d even. This result is a
high-dimensional analogue of the Walker conjecture which was proven by Farber,
Hausmann and the author.
