Skein module dimensions of mapping tori of the 2-torus

We determine the dimension of the Kauffman bracket skein module at generic q for mapping tori of the 2-torus, generalizing the well known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology of the G -skein algebra for G = \mathrm{SL}_{N} or \mathrm{GL}_{N} , which is a direct summand of the whole skein module, and from which the dimensions follow easily in the cases G = \mathrm{SL}_{2} and G = \mathrm{GL}_{1} .