Framings of Links in 3-manifolds and Torsion in Skein Modules

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 admits 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 express our results in the language of skein modules. In particular, we relate our results to the framing skein module and the Kauffman bracket skein module.

algebraic topologydifferential geometrygeneral topologygeometric topology

Audience: researchers in the discipline

GOATS

Series comments: Description: A series of online mini-conferences for graduate students in Geo

Conference will be on Zoom and simultaneously livestreamed to Youtube. Zoom link is obtained by registering on the website, the livestream link will be posted closer to conference date.