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arXiv · 1804.09191

On the uniqueness of polynomial embeddings of the real 1-sphere in the plane

Gene Freudenburg
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Abstract

This paper considers real forms of closed algebraic $\mathbb{C}^*$-embeddings in $\mathbb{C}^2$. The classification of such embeddings was recently completed by Cassou-Nogues, Koras, Palka and Russell. Based on their classification, this paper shows that, up to an algebraic change of coordinates, there is only one polynomial embedding of the real 1-sphere $\mathbb{S}^1$ in the affine plane $\mathbb{R}^2$.

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Gene Freudenburg. 2018-04-24. On the uniqueness of polynomial embeddings of the real 1-sphere in the plane. https://arxiv.org/abs/1804.09191

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