A number theoretic classification of toroidal solenoids

Abstract

We classify toroidal solenoids defined by non-singular $n\times n$-matrices $A$ with integer coefficients by studying associated first Ĉech 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 $n$.

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