## Algebraic & Geometric Topology

### Intersection homology of linkage spaces in odd-dimensional Euclidean space

Dirk Schütz

#### 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. 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 483-508.

Dates
Revised: 22 April 2015
Accepted: 7 May 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841113

Digital Object Identifier
doi:10.2140/agt.2016.16.483

Mathematical Reviews number (MathSciNet)
MR3470706

Zentralblatt MATH identifier
1344.55002

#### Citation

Schütz, Dirk. Intersection homology of linkage spaces in odd-dimensional Euclidean space. Algebr. Geom. Topol. 16 (2016), no. 1, 483--508. doi:10.2140/agt.2016.16.483. https://projecteuclid.org/euclid.agt/1510841113

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