Riemann-Hurwitz formula for Morita-Mumford classes and surface symmetries
The Morita-Mumford classes \(e_n(C_G)\in H^{2n}(G;\mathbb{Z})\) of the homotopy quotient (or the Borel construction) \(C_G\) of the action of a finite group \(G\) on the compact Riemann surface \(C\) in terms of fixed-point data are described. This fixed-point formula is deduced from a higher analogue of the classical Riemann-Hurwitz formula based on computations of \textit{E. Y. Miller} [J. Differ. Geom. 24, 1-14 (1986; Zbl 0618.57005)] and \textit{S. Morita} [Invent. Math. 90, 551-577 (1987; Zbl 0608.57020); Ann. Inst. Fourier 39, No. 3, 777-810 (1989; Zbl 0672.57015); Families of Jacobian manifolds and characteristic classes of surface bundles II, Math. Proc. Camb. Philos. Soc. 105, No. 1, 79-101 (1989); see also Zbl 0619.57012; Invent. Math. 111, No. 1, 197-224 (1993; Zbl 0787.57008)].
scientific article; zbMATH DE number 1286739
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