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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Proper knot theory in open $ 3$-manifolds


Authors: Peter Churchyard and David Spring
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0946435-9
Article copyright: © Copyright 1988 American Mathematical Society