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# Classical Analysis (Leader: Prof. Boris Shekhtman <shekhtma (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'shekhtma' + '&#64;' + 'usf.edu' + '">Prof. Boris Shekhtman</a>');)

## Tuesday, August 3, 2010

Title
Speaker

Time
Place

A solution to the Gromov-Vaserstein Problem
Frank Kutzschebauch
University of Berne
Switzerland
1:00pm-2:00pm
PHY 108

Abstract

Any matrix in $$\operatorname{Sl}_n\,(\mathbb{C})$$ 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 $$X\to\mathbb{C}$$ 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 $$\mathbb{C}^m$$ 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.