The Kauffman Bracket Skein Module

Kauffman bracket skein modules occupy a special place in the panorama of skein modules, standing out as tall mountains in a lush mathematical landscape. In this lecture we will discuss properties of the Kauffman bracket skein module, focusing on their structure and the significance of the presence of torsion in these modules. Witten’ finiteness conjecture and its generalization about the structure of skein modules play a central role in this discussion. We also provide several examples of 3-manifolds for which the Kauffman bracket skein module has been computed and briefly review the relative version of this module.