The topology of local quaternionic toric actions

Panagiotis Batakidis; Ioannis Gkeneralis

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arXiv · 2512.07707

The topology of local quaternionic toric actions

Panagiotis Batakidis·Ioannis Gkeneralis

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Abstract

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.

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BibTeX RIS

Panagiotis Batakidis, Ioannis Gkeneralis. 2026-06-05. The topology of local quaternionic toric actions. https://arxiv.org/abs/2512.07707

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