Covering surfaces

[摘要] Certain parts of the theory of covering surfaces are treated briefly in the literature as they occur in connection with other topics, but very little has been written on the subject itself, particularly in English. Besides being of interest in itself, the subject of covering surfaces has important applications in other fields of mathematics, especially in the study of Riemann surfaces. As is the case with any discussion of a topic in mathematics, the treatment here is merely an introduction. Sections 2 through 6 are concerned with unbranched coverings; the universal covering is studied thoroughly and then follows a brief treatment of regular unbranched coverings in general. The last two sections give a definition of regularly branched coverings and a consideration of the possible simply connected regularly branched coverings. The author *wishes to express his indebtedness to Professor G. R. MacLane, without whose guidance the work would never have been accomplished.

[发布机构] Rice University