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Symmetries of hyperbolic spatial graphs and realization of graph symmetries

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Abstract

In a closed connected orientable 3-manifold associated with an orientation-preserving smooth finite group action, we construct setwise invariant hyperbolic spatial graphs with given singularity. As an application, we provide a condition under which symmetries of abstract graphs are realizable by symmetries of the 3-sphere through hyperbolic spatial embeddings.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 20K03597. The author would like to thank the referee for some helpful comments and suggestions.

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  1. Department of Mathematics, Kindai University, 3-4-1 Kowakae, Higashi-Osaka, Osaka,  577-8502, Japan

    Toru Ikeda

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  1. Toru Ikeda
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Correspondence to Toru Ikeda.

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Ikeda, T. Symmetries of hyperbolic spatial graphs and realization of graph symmetries. J. Geom. 115, 12 (2024). https://doi.org/10.1007/s00022-023-00711-4

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  • DOI: https://doi.org/10.1007/s00022-023-00711-4

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