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arXiv · 1212.3547

Harer stability and orbifold cohomology

Nicola Pagani
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Abstract

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 $g \to \infty$ 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 $\mathcal{M}_{g,n}$.

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Nicola Pagani. 2012-12-14. Harer stability and orbifold cohomology. https://doi.org/10.2140/pjm.2014..101

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