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

Petr Dunin-Barkowski; Alexander Popolitov; George Shabat; Alexei Sleptsov

doi:10.1016/j.difgeo.2015.01.007

paper

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

arXiv:1006.4322 · doi:10.1016/j.difgeo.2015.01.007

Abstract

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

15 pages, 12 figures; proof added, corrections

References in corpus (1)

The Gorenstein conjecture fails for the tautological ring of $M ˉ_{2, n}$

Cited by in corpus (1)

Diagonal complexes