A unified approach to embeddings of a line in 3-space

Drew Lewis

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arXiv · 2203.08178

A unified approach to embeddings of a line in 3-space

Drew Lewis

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Abstract

While the general question of whether every closed embedding of an affine line in affine $3$-space can be rectified remains open, there have been several partial results proved by several different means. We provide a new approach, namely constructing (strongly) residual coordinates, that allows us to give new proofs of all known partial results, and in particular generalize the results of Bhatwadekar-Roy and Kuroda on embeddings of the form $(t^n,t^m,t^l+t)$.

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Drew Lewis. 2022-03-15. A unified approach to embeddings of a line in 3-space. https://arxiv.org/abs/2203.08178

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