Gyration Stability for Products
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913065048473600 |
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| author | Chenery, Sebastian |
| author_facet | Chenery, Sebastian |
| contents | A gyration is an operation on Poincaré Duality complexes that arises from a certain surgery on the product of a given complex $N$ and a sphere, parametrised by a chosen twisting. Of particular recent interest is the notion of gyration stability; that is, $N$ is gyration stable when all of its gyrations have the same homotopy type, regardless of the twisting used. We prove that a product $N\times M$ of two Poincaré Duality complexes is gyration stable when one of the product terms is itself gyration stable, and provide some examples of interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gyration Stability for Products Chenery, Sebastian Algebraic Topology Primary 57N65, Secondary 57P10, 55P15 A gyration is an operation on Poincaré Duality complexes that arises from a certain surgery on the product of a given complex $N$ and a sphere, parametrised by a chosen twisting. Of particular recent interest is the notion of gyration stability; that is, $N$ is gyration stable when all of its gyrations have the same homotopy type, regardless of the twisting used. We prove that a product $N\times M$ of two Poincaré Duality complexes is gyration stable when one of the product terms is itself gyration stable, and provide some examples of interest. |
| title | Gyration Stability for Products |
| topic | Algebraic Topology Primary 57N65, Secondary 57P10, 55P15 |
| url | https://arxiv.org/abs/2604.24301 |