Calculating the Euler characteristic of the moduli space of curves

Bodo Lass (1)

1 CTN - Combinatoire, théorie des nombres

The orbifold Euler characteristic of the moduli space M g;1 of genus g smoth curves with one marked point (g ≥ 1) was calculated by Harer and Zagier: χ(M g;1) = ζ(1 − 2g) = −B 2g /(2g), where ζ is the Riemann zeta function and B 2g is the (2g)th Bernoulli number. We want to make their proof shorter and more combinatorial.

Domaines: Mathématiques [math]

Bodo Lass. Calculating the Euler characteristic of the moduli space of curves. Combinatorica, 2022, 42, pp.749-762. ⟨10.1007/s00493-021-4688-1⟩. ⟨hal-02387454⟩