The topology of local quaternionic toric actions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911308395315200 |
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| author | Batakidis, Panagiotis Gkeneralis, Ioannis |
| author_facet | Batakidis, Panagiotis Gkeneralis, Ioannis |
| contents | In this paper we examine the topology of manifolds equipped with a local quaternionic toric action modeled on the regular representation of the quaternionic torus $Q^n=(S^3)^n$. Building on our previous work, where the toric, differential and tetraplectic foundations were established, we show that the global topology of such manifolds is determined by the orbit space and its characteristic data. We construct Leray--Serre and Atiyah--Hirzebruch spectral sequences for the orbit projection, yielding explicit descriptions of the cohomology and $K$-theory of manifolds equipped with local quaternionic toric actions. In dimension four, we develop a quaternionic analogue of the Meyer signature formula and we briefly outline an $L$-theoretic interpretation of the resulting signature invariants. These results extend the methods of the classical (complex) toric topology to the quaternionic setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_07707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The topology of local quaternionic toric actions Batakidis, Panagiotis Gkeneralis, Ioannis Geometric Topology Algebraic Topology Differential Geometry 57S25, 55T10, 57R18, 57N65 In this paper we examine the topology of manifolds equipped with a local quaternionic toric action modeled on the regular representation of the quaternionic torus $Q^n=(S^3)^n$. Building on our previous work, where the toric, differential and tetraplectic foundations were established, we show that the global topology of such manifolds is determined by the orbit space and its characteristic data. We construct Leray--Serre and Atiyah--Hirzebruch spectral sequences for the orbit projection, yielding explicit descriptions of the cohomology and $K$-theory of manifolds equipped with local quaternionic toric actions. In dimension four, we develop a quaternionic analogue of the Meyer signature formula and we briefly outline an $L$-theoretic interpretation of the resulting signature invariants. These results extend the methods of the classical (complex) toric topology to the quaternionic setting. |
| title | The topology of local quaternionic toric actions |
| topic | Geometric Topology Algebraic Topology Differential Geometry 57S25, 55T10, 57R18, 57N65 |
| url | https://arxiv.org/abs/2512.07707 |