1 results
On framings of links in 3-manifolds
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 4 / December 2021
- Published online by Cambridge University Press:
- 21 September 2020, pp. 752-764
- Print publication:
- December 2021
-
- Article
- Export citation
-
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.
