2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179373We clarify the relation between the Dixmier-Douady class on the space of self adjoint Fredholm operators (`universal B-field') and the curvature of determinant bundles over infinite-dimensional Grassmannians. In particular, in the case of Dirac type operators on a three dimensional compact manifold we obtain a simple and explicit expression for both forms.13 pages, no figuresHigh Energy Physics - TheoryDifferential Geometrytext