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arXiv · 1006.4322

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

Petr Dunin-Barkowski·Alexander Popolitov·George Shabat·Alexei Sleptsov
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Abstract

We suggest a general method of computation of the homology of certain smooth covers $\hat{\mathcal{M}}_{g,1}(\mathbb{C})$ 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 $\mathcal{M}_{g,1}\br{\mathbb{C}}$. 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.

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Petr Dunin-Barkowski, Alexander Popolitov, George Shabat, Alexei Sleptsov. 2011-12-27. On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves. https://doi.org/10.1016/j.difgeo.2015.01.007

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