2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62586We present classical and generalized Riemann-Hilbert problem in several contexts arising from $K$-theory and bordism theory. The language of Fredholm pairs turns out to be useful and unavoidable. We propose an abstract formulation of a notion of bordism in the context of Hilbert spaces equipped with splittings.AMS-tex, 16 pages, 1 figure. to appear in Bull. Polish Acad. Sci. MathK-Theory and HomologyAnalysis of PDEsPrimary 58J55, 55N15; Secondary 58J32, 35J55text