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The cohomology of the moduli space of curves. (English) Zbl 0707.14020

Theory of moduli, Lect. 3rd Sess. Cent. Int. Mat. Estivo, Montecatini Terme/Italy 1985, Lect. Notes Math. 1337, 138-221 (1988).
[For the entire collection see Zbl 0638.00010.]
This article is a survey paper dealing with some topological and geometrical aspects of the moduli space of curves. Some papers of the author and work of Scott Wolpert on the Weil-Petersson geometry of moduli space are discussed. The main question is how much of the topology and formal geometry of a symmetric space can be found for the Teichmüller space and how many of properties of arithmetical group can be found for the mapping class group.
Reviewer: E.Bujalance

MSC:

14H10 Families, moduli of curves (algebraic)
30F60 Teichmüller theory for Riemann surfaces

Citations:

Zbl 0638.00010