On framings of links in 3-manifolds

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.

12 pages, 9 figures

References in corpus (2)

• Skein modules of 3-manifolds
• Homeomorphisms which are Dehn twists on the boundary

Cited by in corpus (2)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Torsion in Kauffman bracket skein module of a $4$-strand Montesinos knot exterior