Proper knot theory in open 3-manifolds

Churchyard, Peter; Spring, David

doi:10.1090/S0002-9947-1988-0946435-9

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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