English

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