Resumen de The abelianization of a symmetric mapping class group
Let Sg,r be a compact oriented surface of genus g with r boundary components. We determine the abelianization of the symmetric mapping class group (g,r)(p2) of a double unbranched cover p2: S2g - 1,2r ? Sg,r using the Riemann constant, Schottky theta constant, and the theta multiplier. We also give lower bounds on the order of the abelianizations of the level d mapping class group.
