Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups
These results generalize from dimension 1 to dimension 2 the second author's results on covering spaces of solenoids. Compact, connected 1-dimensional Abelian groups are constructed as inverse limits of circles. Compact, connected, 2-dimensional Abelian groups \(G\) are constructed as inverse limits of 2-dimensional tori. The authors reduce the problem of classifying finite \(s\)-sheeted covering spaces of such groups \(G\) to the classification of \(s\)-index torsionfree supergroups of the Pontryagin dual \(\widehat G\) of \(G\). This classification allows them to count the number of inequivalent covers in terms of the number theoretic properties of the entries in the \(2\times 2\) matrices that describe the bonding maps of the inverse limit.
scientific article; zbMATH DE number 5013521