B. Bojarski, G. Khimshiashvili

Global Geometric Aspects of Riemann-Hilbert Problems

abstract:
We discuss some global properties of an abstract geometric model for Riemann--Hilbert problems introduced by the first author. In par\-ti\-cu\-lar, we compute the homotopy groups of elliptic Riemann--Hilbert problems and describe some connections with the theory of Fredholm structures which enable one to introduce more subtle geometrical and topological invariants for families of such problems.