Skein modules and framing changes for links in 3-manifolds

Rhea Palak Bakshi (George Washington University)

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 admits a properly embedded non-separating . 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 express our results in the language of skein modules. In particular, we relate our results to the presence of torsion in the framing skein module.