On actions of tori and quaternionic tori on products of spheres
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914312442871808 |
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| author | Ayzenberg, Anton Gugnin, Dmitry |
| author_facet | Ayzenberg, Anton Gugnin, Dmitry |
| contents | In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to a sphere. A similar statement for a real torus $\mathbb{Z}_2^n$ was proved by the second author in 2019. We also provide a statement about arbitrary compact topological groups, generalizing the mentioned results, as well as the results of the first author about the actions of a compact torus of complexity one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05611 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On actions of tori and quaternionic tori on products of spheres Ayzenberg, Anton Gugnin, Dmitry Algebraic Topology 57S12, 57S15, 57S25 (Primary) 57R10 (Secondary) In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to a sphere. A similar statement for a real torus $\mathbb{Z}_2^n$ was proved by the second author in 2019. We also provide a statement about arbitrary compact topological groups, generalizing the mentioned results, as well as the results of the first author about the actions of a compact torus of complexity one. |
| title | On actions of tori and quaternionic tori on products of spheres |
| topic | Algebraic Topology 57S12, 57S15, 57S25 (Primary) 57R10 (Secondary) |
| url | https://arxiv.org/abs/2309.05611 |