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Intersection homology of linkage spaces in odd dimensional Euclidean space.

Schuetz, Dirk (2016) 'Intersection homology of linkage spaces in odd dimensional Euclidean space.', Algebraic & geometric topology., 16 (1). pp. 483-508.


We consider the moduli spaces Md(ℓ)ℳd(ℓ) of a closed linkage with nn links and prescribed lengths ℓ∈Rnℓ∈ℝn in dd–dimensional Euclidean space. For d>3d>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)ℳd(ℓ) for a large class of length vectors. These rings behave rather differently depending on whether dd 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.

Item Type:Article
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Publisher statement:First published in Geometry & Topology in 16 (2016) 483–508, published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.
Date accepted:14 May 2015
Date deposited:19 January 2016
Date of first online publication:23 February 2016
Date first made open access:No date available

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