#### Volume 16, issue 1 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Intersection homology of linkage spaces in odd-dimensional Euclidean space

### Dirk Schütz

Algebraic & Geometric Topology 16 (2016) 483–508
##### Abstract

We consider the moduli spaces ${\mathsc{ℳ}}_{d}\left(\ell \right)$ of a closed linkage with $n$ links and prescribed lengths $\ell \in {ℝ}^{n}$ in $d\phantom{\rule{0.3em}{0ex}}$–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 ${\mathsc{ℳ}}_{d}\left(\ell \right)$ for a large class of length vectors. These rings behave rather differently depending on whether $d$ 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.