A number theoretic classification of toroidal solenoids

We classify toroidal solenoids defined by non-singular $n\times n$-matrices $A$ with integer coefficients by studying associated first \^Cech cohomology groups. In a previous work, we classified the groups in the case $n=2$ using generalized ideal classes in the splitting field of the characteristic polynomial of $A$. In this paper we explore the classification problem for an arbitrary $n$.