Intersection homology of linkage spaces in odd dimensional Euclidean space

Schuetz, Dirk

Abstract

We consider the moduli spaces Md(ℓ)ℳd(ℓ) of a closed linkage with nn links and prescribed lengths ℓ∈Rnℓ∈ℝn in dd–dimensional Euclidean space. For d>3d>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)ℳd(ℓ) for a large class of length vectors. These rings behave rather differently depending on whether dd is even or odd, with the even case having been treated in an earlier paper. The main difference in the odd case comes from an extra generator in the ring, which can be thought of as an Euler class of a stratified bundle.

Citation

Schuetz, D. (2016). Intersection homology of linkage spaces in odd dimensional Euclidean space. Algebraic & geometric topology, 16(1), 483-508. https://doi.org/10.2140/agt.2016.16.483

• Journal Article Type: Article
• Acceptance Date: May 14, 2015
• Online Publication Date: Feb 23, 2016
• Publication Date: Feb 23, 2016
• Deposit Date: Jan 7, 2016
• Publicly Available Date: Jan 19, 2016
• Journal: Algebraic and Geometric Topology
• Print ISSN: 1472-2747
• Electronic ISSN: 1472-2739
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 1
• Pages: 483-508
• DOI: https://doi.org/10.2140/agt.2016.16.483
• Public URL: https://durham-repository.worktribe.com/output/1395269