2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62052The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and an arbitrary coefficient ring R. If R is regular this leads to a concrete calculation of low dimensional K-theory groups of RG in terms of the K-theory of R and the homology of the group.64 pagesAlgebraic TopologyGeometric TopologyK-Theory and Homology19A31, 19B28, 19D35, 19D50text