Roberto Ferreiro Perez
On the first Pontryagin form of a surface
The universal first Pontryagin form of a compact surface is a 4-form on the first jet bundle of the bundle of Riemannian metric. This form determines a canonical pre-symplectic structure and moment map on the space of Riemannian metrics.
The corresponding Marsden-Weinstein quotient is the Teichmüller space of the surface endowed with the Weil-Petersson symplectic form.