Tara Brendle, Cornell University, November 26, 2002
Title: On the linearity question for mapping class groups (joint work with Hessam Hamidi-Tehrani)
Abstract:
Formanek and Procesi proved in 1992 that Aut(F_n) is not linear if $n \geq
3$. However, the linearity question remains unsettled for mapping class
groups of surfaces, which in many respects are similar to Aut(F_n). We
will discuss Formanek and Procesi's method for constructing certain
subgroups of Aut(F_n) which are obstructions to linearity. We then show
that such groups do not embed in mapping class groups. Thus, the only
technique available for possibly proving that mapping class groups are not
linear actually fails, giving strong evidence that mapping class groups
may in fact be linear.