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arXiv · 2609.17340

Fixed Point Theorems in Quaternionic Geometry

Niklas Henningsen
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Abstract

We consider an application of the Atiyah-Bott fixed point theorem in quaternionic geometry. We review the relation of the general Salamon complex of a quaternionic manifold and the Dolbeault complex with coefficients in a certain holomorphic vector bundle of its twistor space. Furthermore, we investigate which maps are suitable for the application of the fixed point theorem. As a result, we obtain a fixed point formula for both complexes and apply it to Wolf spaces.

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Niklas Henningsen. 2026-09-15. Fixed Point Theorems in Quaternionic Geometry. https://arxiv.org/abs/2609.17340

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