Long line knots

Original · EN

We study continuous embeddings of the long line L into Lⁿ (n>1) up to ambient isotopy of Lⁿ. 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 → L³ is equivalent to the classification of classical oriented knots.