2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185745K-theory allows us to define an analytical condition for the existence of `false' gauge field copies through the use of the Atiyah-Singer index theorem. After establishing that result we discuss a possible extension of the same result without the help of the index theorem and suggest possible related lines of work.LaTeX, 7 pages, no figuresMathematical PhysicsK-Theory and Homologytext