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Intersection homology of linkage spaces in odd-dimensional Euclidean space

Dirk Schütz

Algebraic & Geometric Topology 16 (2016) 483–508

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.

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