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Fixed Point Theorems in Quaternionic Geometry
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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BibTeX
@misc{henningsen2026fixed,
title = {{Fixed Point Theorems in Quaternionic Geometry}},
author = {Niklas Henningsen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17340},
eprint = {2609.17340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17340},
}
RIS
TY - UNPB
TI - Fixed Point Theorems in Quaternionic Geometry
AU - Niklas Henningsen
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17340
UR - https://arxiv.org/abs/2609.17340
AB - 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.
ER -