In [13], Gilmer and Masbaum use Witten-Reshetikhin-Turaev (WRT) invariants to define a map from the Kauffman bracket skein module to a set of complex-valued functions defined on roots of unity in order to provide a lower bound for its dimension. We show that the restriction of the map to a certain homology class is not injective. We also provide a basis for the KBSM of mapping tori associated to a power of a Dehn twist on the 2-torus.

This work was partially supported by the ANER "CLICQ" of the Region Bourgogne Franche-Comte. The IMB receives support from the EIPHI Graduate School (contract ANR-17-EURE-0002).