Geodesic
Intersection homology of linkage spaces in odd-dimensional Euclidean space
Schütz, Dirk1
1Department of Mathematics, University of Durham, South Road, Durham DH1 3LE, UK
Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 483-508
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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.

DOI : 10.2140/agt.2016.16.483
Classification : 55R80, 55N33, 55N45
Keywords: configuration spaces, linkages, intersection homology

Schütz, Dirk  1

1 Department of Mathematics, University of Durham, South Road, Durham DH1 3LE, UK 
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Schütz, Dirk. Intersection homology of linkage spaces in odd-dimensional Euclidean space. Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 483-508. doi: 10.2140/agt.2016.16.483

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