Geometry Topology Seminar
Monday, January 23, 2017 - 14:05
1 hour (actually 50 minutes)
The point-pushing subgroup of the mapping class group of a surface with a marked point can be considered topologically as the subgroup that pushes the marked point about loops in the surface. Birman demonstrated that this subgroup is abstractly isomorphic to the fundamental group of the surface, \pi_1(S). We can characterize this point-pushing subgroup algebraically as the only normal subgroup inside of the mapping class group isomorphic to \pi_1(S). This uniqueness allows us to recover a description of the outer automorphism group of the mapping class group.