Geometry of extensions of free groups via automorphisms with fixed points on the complex of free factors
| Autor: | Ghosh, Pritam, Gültepe, Funda |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give conditions of an extension of a free group to be hyperbolic and relatively hyperbolic using the dynamics of the action of $\out$ on the complex of free factors combined with the weak attraction theory. We work with subgroups of exponentially growing outer automorphisms and instead of using a standard pingpong argument with loxodromics, we allow fixed points for the action and investigate the geometry of the extension group when the fixed points of the automorphisms on the complex of free factors are sufficiently far apart. Comment: 33 pages. This is the sequel to arXiv:2307.09674v2, which has now been divided into two parts. This part consists of the second half of the original version arXiv:2307.09674v2 where we included the hyperbolicity and relative hyperbolicity of the free group extensions using the action on the complex of free factors |
| Databáze: | arXiv |
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