Theoretical Statistics and Mathematics Unit, ISI Delhi
Let F be a field and G be a simple and simply connected group over F (e.g. G=SL(n) ). Kneser-Tits conjecture asserts that if G(F) contains non-trivial unipotents, then G(F) is simple modulo its center. The conjecture is well known to be false. The obstruction to validity of the conjecture lies in the Whitehead group of G. This group fits in a K-theoretic set up for G.
Hence one is interested in computing this obstruction. If this obstruction is trivial, then G(F) is simple modulo its center, providing interesting examples of infinite (abstract) simple groups. We will discuss a geometric notion called R-equivalence for algebraic groups, due to Manin and mention a link with Whitehead groups and finally report on some recent work on the problem.