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

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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.

##### Keywords
configuration spaces, linkages, intersection homology
##### Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 55N33, 55N45
##### Publication
Received: 24 October 2014
Revised: 22 April 2015
Accepted: 7 May 2015
Published: 23 February 2016
##### Authors
 Dirk Schütz Department of Mathematics University of Durham South Road Durham DH1 3LE UK