Riemann-Hilbert problem: K-theory and bordisms

Bogdan Bojarski and Andrzej Weber

We present classical and generalized Riemann-Hilbert problem in several context 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.