The Johnson kernels are the subgroups of the mapping class group which act trivially on the quotient of the surface group module terms of the lower central series; for instance, the first Johnson kernel is the Torelli group. We prove that the abstract commensurator of every Johnson kernel is the full mapping class group. This is joint work with Martin Bridson and Alexandra Pettet.

For more information, contact Khalid Bou-Rabee khalidb[at]umich(dot)edu