Overcommuting pairs in groups and 3-manifolds bounding them
arXiv:1903.11418 · doi:10.1112/jlms.12359
Abstract
We introduce the notions of overcommutation and overcommutation length in groups, and show that these concepts are closely related to representations of the fundamental groups of 3-manifold and their Heegaard genus. We give many examples including translations in the affine group of the line and provide upper bounds for the overcommutation length in SL_2, related to the Steinberg relation.
arXiv comment19 pages, 1 figure