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A generalization of the lightbulb theorem and PL $ I$-equivalence of links


Author: Rick Litherland
Journal: Proc. Amer. Math. Soc. 98 (1986), 353-358
MSC: Primary 57Q45
DOI: https://doi.org/10.1090/S0002-9939-1986-0854046-2
MathSciNet review: 854046
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Abstract: By the "lightbulb theorem" I mean the result that a knot of $ {S^1}$ in $ {S^1} \times {S^2}$ which meets some $ {S^2}$ factor in a single transverse point is isotopic to an $ {S^1}$ factor. We prove an analogous result for knots of $ {S^n}$ in $ {S^n} \times {S^2}$, and apply it to answer a question of Rolfsen concerning PL I-equivalence of links.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0854046-2
Article copyright: © Copyright 1986 American Mathematical Society

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