The Euler characteristic of the moduli space of curves

@article{Harer1986TheEC,
  title={The Euler characteristic of the moduli space of curves},
  author={J. Harer and Don Zagier},
  journal={Inventiones mathematicae},
  year={1986},
  volume={85},
  pages={457-485}
}
Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be its Euler characteristic in the sense of Wall, that is Z(F~I)= [Fgl: F] l z(E/F), where F is any torsion free subgroup of finite index in F~ 1 and E is a contractible space on which F acts freely and properly discontinuously. An example of such a space is the Teichmiiller space ~-~1, and g(F~ ~) can be… 
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