**G. Khimshiashvili**

## Hyper-Holomorphic Cells and Fredholm Theory

**abstract:**

We deal with differentiable cells defined by solutions
to certain linear elliptic systems of first order. It turns out
that in some cases families of such cells attached to a given submanifold
may be described by Fredholm operators in appropriate function
spaces. Using the previous results of the author on the existence of
elliptic Riemann--Hilbert problems for generalized Cauchy--Riemann
systems, we indicate some classes of systems which give rise to
non-linear Fredholm operators of such type.