Abstract
We investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine \({H^k\left({\bar S}_{g}, {\mathbb Q}\right)}\) for g ≥ 2 and k ≤ 3, where \({{\bar S}_{g}}\) denotes the moduli space of spin curves of genus g.
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