Pontryagin forms on $(4k-2)$-manifolds and symplectic structures on the spaces of Riemannian metrics

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220283The Pontryagin forms on 1-jet bundle of Riemannian metrics, are shown to provide, in a natural way, diffeomorphism-invariant pre-symplectic structures on the space of Riemannian metrics for dimensions $n=4r-2$. The equivariant Pontryagin forms provide canonical moment maps for these structures. In dimension two, the symplectic reduction corresponding to the pre-symplectic form and its moment map attached to the first Pontryagin form, is proved to coincide with the Teichmüller space endowed with the Weil-Petersson symplectic form.Differential Geometry53D30 (Primary) 55R40, 58A20, 58D17 (Secondary)Pontryagin forms on $(4k-2)$-manifolds and symplectic structures on the spaces of Riemannian metricstext