Non-lifting of a subgroup of the mapping class group

Geometry Topology Student Seminar
Wednesday, December 4, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
The mapping class group of a surface is a quotient of the group of orientation preserving diffeomorphisms.  However the mapping class group generally can't be lifted to the group of diffeomorphisms, and even many subgroups can't be lifted.  Given a surface S of genus at least 2 and a marked point z, the fundamental group of S naturally injects to a subgroup of MCG(S,z).  I will present a result of Bestvina-Church-Souto that this subgroup can't be lifted to the diffeomorphisms fixing z.