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Long line knots

Mathieu Baillif·David Cimasoni
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Abstract

We study continuous embeddings of the long line L into L^n (n>1) up to ambient isotopy of L^n. We define the direction of an embedding and show that it is (almost) a complete invariant in the case n=2 for continuous embeddings, and in the case n>3 for differentiable ones. Finally, we prove that the classification of smooth embeddings L \to L^3 is equivalent to the classification of classical oriented knots.

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Mathieu Baillif, David Cimasoni. 2004-06-09. Long line knots. https://arxiv.org/abs/math/0406179

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