Distribution of branched ¢Dp-coverings of surfaces

✍ Scribed by Jin Ho Kwak; Jaeun Lee

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 804 KB
• Volume: 183
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(97)00030-7

✦ Synopsis

A well-known theorem of Alexander [1] says that every orientable surface is a branched covering of the sphere N2, and every nonorientable surface is a branched covering of the projective plane. In the study of surface branched coverings [2,3, 14], we can ask naturally as a generalization of Alexander's theorem: In how many d(lZJbrent ways can a given surface be a branched covering of another 9iven surJace?

As a partial answer of this question, Kwak et al., recently enumerated the equivalence classes of regular branched prime-fold coverings p : ~ --, N for any given surfaces S and ~. In this paper, we aim to enumerate the equivalence classes of the regular branched surface coverings p : ~; ~ 5 whose covering transformation group is the dihedral group [Dp of order 2p, p prime. In some sense, this gives a classification of the pseudo-free De-actions on a surface when a data for a quotient surface is given.