Note on the deck transformations group and the monodromy group (Q701320)

This cute paper compares two groups associated to branched coverings between Riemann surfaces. The first group ``Mon'' (monodromy) comes from the action of the fundamental group of the base on the sheets of the covering. The second group ``Deck'' consists of automorphisms over the base. The author describes these groups in details and discusses their relation to the Galois theory of the extension of fields determined by the cover, as well as to more recent aspects of complex function theory and integrals. The content is semi-expository and especially rich in examples. The core ideas should be known to experts, although it is useful to have them summarized and proven is one reference.