Overcommuting pairs in groups and 3‐manifolds bounding them
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‐manifolds and their Heegaard genus. We give many examples including translations in the affine group of the line and pr...
Gespeichert in:
Veröffentlicht in: | Journal of the London Mathematical Society 2020-12, Vol.102 (3), p.1160-1177 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | 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‐manifolds 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 SL2, related to the Steinberg relation. |
---|---|
ISSN: | 0024-6107 1469-7750 |
DOI: | 10.1112/jlms.12359 |