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The Minimal Dimension of a Sphere with an Equivariant Embedding of the Bouquet of g Circles is \(2g-1\)

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Abstract

To embed the bouquet of g circles \(B_g\) into the n-sphere \(S^n\) so that its full symmetry group action extends to an orthogonal actions on \(S^n\), the minimal n is \(2g-1\). This answers a question raised by Zimmermann.

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Acknowledgements

We thank the referees for their suggestions which enhanced the paper.

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  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100080, China

    Zhongzi Wang

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  1. Zhongzi Wang
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Correspondence to Zhongzi Wang.

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Wang, Z. The Minimal Dimension of a Sphere with an Equivariant Embedding of the Bouquet of g Circles is \(2g-1\). Discrete Comput Geom 67, 1257–1265 (2022). https://doi.org/10.1007/s00454-021-00300-9

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  • DOI: https://doi.org/10.1007/s00454-021-00300-9

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