Long line knots
Abstract
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.
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