2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161836In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular, the role that the multiplicity of eigenvalues plays is developed here.Typos fixed and application improvedK-Theory and Homology19K56;46L80text