Corpus ID: 210859354

On framings of knots in 3-manifolds.

@inproceedings{Bakshi2020OnFO,
  title={On framings of knots in 3-manifolds.},
  author={Rhea Palak Bakshi and Dionne Ibarra and Gabriel Montoya-Vega and J{\'o}zef H. Przytycki and Deborah Weeks},
  year={2020}
}
  • Rhea Palak Bakshi, Dionne Ibarra, +2 authors Deborah Weeks
  • Published 2020
  • Mathematics
  • We show that the only way of changing the framing of a knot or 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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