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Durham University

Department of Mathematical Sciences

Staff

Publication details for Dirk Schuetz

Schuetz, Dirk (2016). Intersection homology of linkage spaces. Journal of Topology and Analysis 08(01): 25-58.

Author(s) from Durham

Abstract

We consider the moduli spaces ℳd(ℓ) of a closed linkage with n links and prescribed lengths ℓ ∈ 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(ℓ) 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.