Intersection homology of linkage spaces

Abstract

We consider the moduli spaces [Formula: see text] of a closed linkage with [Formula: see text] links and prescribed lengths [Formula: see text] in [Formula: see text]-dimensional Euclidean space. For [Formula: see text] 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 [Formula: see text] for a large class of length vectors in the case of [Formula: see text] even. This result is a high-dimensional analogue of the Walker conjecture which was proven by Farber, Hausmann and the author.