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On framings of links in 3-manifolds
Published online by Cambridge University Press: 21 September 2020
Abstract
We show that the only way of changing the framing of a link by ambient isotopy in an oriented
$3$
-manifold is when the manifold has a properly embedded non-separating
$S^{2}$
. This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough’s work on the mapping class groups of
$3$
-manifolds. We also relate our results to the theory of skein modules.
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- © Canadian Mathematical Society 2020
Footnotes
The fourth author was partially supported by Simons Collaboration Grant-637794 and the CCAS Dean’s Research Chair award.
References
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