Generalized Riemann-Hilbert Transmission and Boundary Value Problems, Fredholm Pairs and Bordisms

Abstract

We 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.