Algebraic & Geometric Topology

Intersection homology of linkage spaces in odd-dimensional Euclidean space

Dirk Schütz

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We consider the moduli spaces d() of a closed linkage with n links and prescribed lengths n 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 d() 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

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

Received: 24 October 2014
Revised: 22 April 2015
Accepted: 7 May 2015
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R80: Discriminantal varieties, configuration spaces
Secondary: 55N33: Intersection homology and cohomology 55N45: Products and intersections

configuration spaces linkages intersection homology


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.

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