Overcommuting pairs in groups and 3-manifolds bounding them

Livio Liechti; Julien Marché

doi:10.1112/jlms.12359

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arXiv · 1903.11418

Overcommuting pairs in groups and 3-manifolds bounding them

Livio Liechti·Julien Marché

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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.

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Livio Liechti, Julien Marché. 2020-12-18. Overcommuting pairs in groups and 3-manifolds bounding them. https://doi.org/10.1112/jlms.12359

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