Canonical 2-forms on the moduli space of Riemann surfaces

Details Canonical 2-forms on the moduli space of Riemann surfaces Canonical 2-forms on the moduli space of Riemann surfaces

2007-08-31

arxiv.org/abs/0708.4271v3

Mathematics

Geometric Topology

Scientific paper

As was shown by Harer the second homology of ${\mathbb M}_g$, the moduli space of compact Riemann surfaces of genus $g$, is of rank 1, provided $g \geq 3$. This means a nontrivial second de Rham cohomology class on ${\mathbb M}_g$ is unique up to constant factor. But several canonical 2-forms on the moduli space have been constructed in various geometric contexts, and differ from each other. In this article we review some of constructions in order to provide materials for future research on "secondary geometry" of the moduli space ${\mathbb M}_g$.

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