2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152259On an open manifold, the spaces of metrics or connections of bounded geometry, respectively, split into an uncountable number of components. We show that for a pair of metrics or connections, belonging to the same component, relative $ζ$-functions, determinants, torsion for pairs of generalized Dirac operators are well defined.Differential Geometrytext