Solution to the Gromov-Vaserstein problem

Any matrix in Sl_n (C) can (due to the Gauss elimination process)
be written as a product of elementary matrices.
If instead of the complex numbers (a field)
the entries in the matrix are elements of a ring, this becomes a delicate question. In particular
the rings of maps from a space X to C are interesting cases. A deep result of Suslin gives an affirmative answer for
the polynomial ring in m variables in case the size of the matrix (n) is greater than 2. In the topological category the
problem was solved by Thurston and Vaserstein. For holomorphic functions on C^m the problem was posed by Gromov
in the 1980's. We report on a complete solution to Gromov's problem. A main tool is the Oka-Grauert-Gromov-h-principle in Complex Analysis.
This is joint work with Björn Ivarsson.