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Intersection homology of linkage spaces in odd dimensional Euclidean space

Schuetz, Dirk

Intersection homology of linkage spaces in odd dimensional Euclidean space Thumbnail


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Abstract

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.

Citation

Schuetz, D. (2016). Intersection homology of linkage spaces in odd dimensional Euclidean space. Algebraic & geometric topology, 16(1), 483-508. https://doi.org/10.2140/agt.2016.16.483

Journal Article Type Article
Acceptance Date May 14, 2015
Online Publication Date Feb 23, 2016
Publication Date Feb 23, 2016
Deposit Date Jan 7, 2016
Publicly Available Date Mar 28, 2024
Journal Algebraic and Geometric Topology
Print ISSN 1472-2747
Electronic ISSN 1472-2739
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 16
Issue 1
Pages 483-508
DOI https://doi.org/10.2140/agt.2016.16.483

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Copyright Statement
First published in Geometry & Topology in 16 (2016) 483–508, published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.




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