Intersection homology of linkage spaces in odd-dimensional Euclidean space

Schütz, Dirk

doi:10.2140/agt.2016.16.483

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Intersection homology of linkage spaces in odd-dimensional Euclidean space

Dirk Schütz

Algebraic & Geometric Topology 16 (2016) 483–508

DOI: 10.2140/agt.2016.16.483

Abstract

We consider the moduli spaces $ℳ_{d} (ℓ)$ of a closed linkage with $n$ links and prescribed lengths $ℓ \in ℝ^{n}$ 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 $ℳ_{d} (ℓ)$ 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.

Keywords

configuration spaces, linkages, intersection homology

Mathematical Subject Classification 2010

Primary: 55R80

Secondary: 55N33, 55N45

References

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

Volume 16, issue 1 (2016)