Hyperbolic one-relator groups
We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising hyperbolic one-relator groups to characterising hyperbolic p...
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| Format: | Journal article |
| Language: | English |
| Published: |
Cambridge University Press
2024
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| Summary: | We introduce two families of two-generator one-relator groups called primitive extension
groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising hyperbolic one-relator groups to characterising
hyperbolic primitive extension groups. These new groups moreover admit explicit decompositions
as graphs of free groups with adjoined roots. In order to obtain this result, we characterise 2-free
one-relator groups with exceptional intersection in terms of Christoffel words, show that hyperbolic one-relator groups have quasi-convex Magnus subgroups and build upon the one-relator tower
machinery developed in previous work of the author. |
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