INTERSECTION HOMOLOGY OF LINKAGE SPACES

Abstract. We consider the moduli spaces Md(`) of a closed linkage with n links and prescribed lengths ` ∈ Rn 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 types of Md(`) 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. 1