## Proper knot theory in open $3$-manifolds

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- by Peter Churchyard and David Spring PDF
- Trans. Amer. Math. Soc.
**308**(1988), 133-142 Request permission

## Abstract:

This paper introduces a theory of proper knots, i.e., smooth proper embeddings of ${{\mathbf {R}}^1}$ into open $3$-manifolds. Proper knot theory is distinguished by the fact that proper isotopies of knots are not ambient in general. A uniqueness theorem for proper knots is proved in case the target manifold is the interior of a one-dimensional handlebody.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**308**(1988), 133-142 - MSC: Primary 57M25; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9947-1988-0946435-9
- MathSciNet review: 946435