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

Litherland, Rick

doi:10.1090/S0002-9939-1986-0854046-2

A generalization of the lightbulb theorem and PL $I$-equivalence of links
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Proc. Amer. Math. Soc. 98 (1986), 353-358 Request permission

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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