Intersection homology of linkage spaces in odd-dimensional Euclidean space
| Autor: | Dirk Schütz |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
55R80 (primary) 55N33
55N45 57R70 (secondary) Structure (category theory) 01 natural sciences Combinatorics Intersection homology 0103 physical sciences FOS: Mathematics 55N33 Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Mathematics Ring (mathematics) intersection homology Euclidean space 010102 general mathematics Homeomorphism Moduli space linkages 55R80 55N45 010307 mathematical physics Geometry and Topology configuration spaces Euler class Generator (mathematics) |
| Zdroj: | Algebr. Geom. Topol. 16, no. 1 (2016), 483-508 Algebraic & geometric topology, 2016, Vol.16(1), pp.483-508 [Peer Reviewed Journal] |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2016.16.483 |
| Popis: | We consider the moduli spaces $\mathcal{M}_d(\ell)$ of a closed linkage with $n$ links and prescribed lengths $\ell\in \mathbb{R}^n$ 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 $\mathcal{M}_d(\ell)$ 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 startified bundle. 19 pages, 1 figure |
| Databáze: | OpenAIRE |
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