On Hurwitz theory: enumerating branched surface coverings

author: Jin Ho Kwak, Pohang University of Science and Technology (POSTECH)
published: Sept. 7, 2007,   recorded: September 2007,   views: 3836

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With a chronological review of Hurwitz theory, we survey some known results on the enumeration of the equivalence classes of several types of branched coverings of a surface. In particular, relations with the enumeration of the equivalence classes of several types of graph coverings and enumerating the isomorphism classes of branched orientable surface coverings of a nonorientable surface will be mentioned. Also we discuss a similar problem for branched coverings having prescribed branched types.

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