Overcommuting pairs in groups and 3-manifolds bounding them
Geometric Topology
2020-12-21 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.1903.11418,
title = {Overcommuting pairs in groups and 3-manifolds bounding them},
author = {Livio Liechti and Julien Marché},
journal= {arXiv preprint arXiv:1903.11418},
year = {2020}
}
Comments
19 pages, 1 figure