Algebraic & Geometric Topology

Intersection homology of linkage spaces in odd-dimensional Euclidean space

Dirk Schütz

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Abstract

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

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

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

Permanent link to this document
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

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

Keywords
configuration spaces linkages intersection homology

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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