Geodesic
On framings of links in 3-manifolds
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 752-764

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DOI

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.
DOI : 10.4153/S000843952000079X
Mots-clés : Knots, links, 3-manifolds, framings of links, skein modules, spin structures, Dehn homeomorphisms, incompressible surfaces 
Bakshi, Rhea Palak; Ibarra, Dionne; Montoya-Vega, Gabriel; Przytycki, Józef H.; Weeks, Deborah. On framings of links in 3-manifolds. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 752-764. doi: 10.4153/S000843952000079X
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     title = {On framings of links in 3-manifolds},
     journal = {Canadian mathematical bulletin},
     pages = {752--764},
     year = {2021},
     volume = {64},
     number = {4},
     doi = {10.4153/S000843952000079X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952000079X/}
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