Mathematical Sciences Geometry/Topology Seminar

November 14:
Speaker: Tara Brendle (Cornell University)
Title: On the linearity question for mapping class groups

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 of constructing certain subgroups of Aut(F_n) which are obstructions to linearity, and 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.