|Sep 27, 2016
Mapping class group is the group of the homotopy classes of orientation-preserving self-homeomorphisms. This group have been studied a lot in low-dimensional topology and geometric group theory. But we still don't know whether mapping class groups are linear. In this talk, I introduce some relations between mapping class groups and linear groups, including the symplectic representation of mapping class groups and the mapping class group of genus 2.