Harer stability and orbifold cohomology

In this paper we review the combinatorics of the twisted sectors of ${\mathcal{M}}_{g,n}$, and we exhibit a formula for the age of each of them in terms of the combinatorial data. Then we show that orbifold cohomology of ${\mathcal{M}}_{g,n}$ when $g\to \mathrm{\infty }$ reduces to its ordinary cohomology. We do this by showing that the twisted sector with minimal age is always the hyperelliptic twisted sector with all markings in the Weierstrass points; the age of the latter moduli space is just half its codimension in ${\mathcal{M}}_{g,n}$.