Long line knots

Details Long line knots Long line knots

2004-06-09

arxiv.org/abs/math/0406179v1

Mathematics

General Topology

11 pages, 4 figures, to appear in Arch. Math. 82 (2004)

Scientific paper

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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