Scientific article
Open access

Long line knots

Published inArchiv der Mathematik, vol. 83, no. 1, p. 70-80
Publication date2004

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 o L^3 is equivalent to the classification of classical oriented knots.

  • arxiv : math.GN
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Citation (ISO format)
BAILLIF, Mathieu, CIMASONI, David. Long line knots. In: Archiv der Mathematik, 2004, vol. 83, n° 1, p. 70–80. doi: 10.1007/s00013-004-4760-2
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Article (Accepted version)
ISSN of the journal0003-889X

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