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- W1978227883 abstract "We study continuous embeddings of the long line $$ textsf{L} $$ into $$ textsf{L}^{n} (n geq 2) $$ up to ambient isotopy of $$ textsf{L}^{n} $$ . 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 $$ n geq 4 $$ for differentiable ones. Finally, we prove that the classification of smooth embeddings $$ textsf{L} to textsf{L}^3 $$ is equivalent to the classification of classical oriented knots." @default.
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- W1978227883 date "2004-07-01" @default.
- W1978227883 modified "2023-10-14" @default.
- W1978227883 title "Long line knots" @default.
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- W1978227883 doi "https://doi.org/10.1007/s00013-004-4760-2" @default.
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