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## On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves

Differential Geometry and its Application. 2015. Vol. 40. P. 86-102.
Dunin-Barkowski P., Popolitov A., Shabat G., Sleptsov A.

We suggest a general method of computation of the homology of certain smooth covers $\widehat{\mathcal{M}}_{g,1}(\mathbb{C})$ of moduli spaces $\mathcal{M}_{g,1}\br{\mathbb{C}}$ of pointed curves of genus $g$. Namely, we consider moduli spaces of algebraic curves with level $m$ structures. The method is based on the lifting of the Strebel-Penner stratification of $\mathcal{M}_{g,1}\br{\mathbb{C}}$. We apply this method for $g\leq 2$ and obtain Betti numbers; these results are consistent with Penner and Harer-Zagier results on Euler characteristics.