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.