open access

https://doi.org/10.14943/83470

https://hdl.handle.net/2115/69074

An infinitesimal approach to the stable cohomology of the moduli of Riemann surfaces

英語

1995-12-01

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

323

1-22

In this note we review an infinitesimal approach to the stable coho­ mology of the moduli of compact Riemann surfaces by means of complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces. Under a hypothesis (a certain kind of the Frobenius Reciprocity Laws) we prove the (p, q)-equivariant cohomology of the dressed moduli of compact Riemann surfaces coincides with the polynomial al­gebra generated by the Morita-Mumford classes en = K.n (n 􀀁 1) [Mo] [Mu] for p 􀀭 q. This suggests it is reasonable to conjecture that the stable cohomology algebra of the moduli of compact Riemann surfaces would be generated by the Morita-Mumford classes en's. For a more detailed description the reader is referred to [Kal,2,4,5].

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