Intersection homology of linkage spaces

Schuetz, Dirk

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.

Citation

Schuetz, D. (2016). Intersection homology of linkage spaces. Journal of Topology and Analysis, 08(01), 25-58. https://doi.org/10.1142/s1793525316500023

• Journal Article Type: Article
• Acceptance Date: Mar 29, 2015
• Online Publication Date: Oct 8, 2015
• Publication Date: Mar 1, 2016
• Deposit Date: Jun 29, 2015
• Publicly Available Date: May 8, 2016
• Journal: Journal of Topology and Analysis
• Print ISSN: 1793-5253
• Electronic ISSN: 1793-7167
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 08
• Issue: 01
• Pages: 25-58
• DOI: https://doi.org/10.1142/s1793525316500023
• Keywords: Configuration spaces, Linkages, Intersection homology.
• Public URL: https://durham-repository.worktribe.com/output/1402983