Relative free splitting and free factor complexes I: Hyperbolicity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| _version_ | 1866915190110420992 |
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| author | Handel, Michael Mosher, Lee |
| author_facet | Handel, Michael Mosher, Lee |
| contents | We study the large scale geometry of the relative free splitting complex and the relative free factor complex of the rank $n$ free group $F_n$, relative to the choice of a free factor system of $F_n$, proving that these complexes are hyperbolic. Furthermore we present the proof in a general context, obtaining hyperbolicity of the relative free splitting complex and of the relative free factor complex of a general group $Γ$, relative to the choice of a free factor system of $Γ$. The proof yields information about coarsely transitive families of quasigeodesics in each of these complexes, expressed in terms of fold paths of free splittings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1407_3508 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Relative free splitting and free factor complexes I: Hyperbolicity Handel, Michael Mosher, Lee Group Theory 20F65 (primary) 57M07 (secondary) We study the large scale geometry of the relative free splitting complex and the relative free factor complex of the rank $n$ free group $F_n$, relative to the choice of a free factor system of $F_n$, proving that these complexes are hyperbolic. Furthermore we present the proof in a general context, obtaining hyperbolicity of the relative free splitting complex and of the relative free factor complex of a general group $Γ$, relative to the choice of a free factor system of $Γ$. The proof yields information about coarsely transitive families of quasigeodesics in each of these complexes, expressed in terms of fold paths of free splittings. |
| title | Relative free splitting and free factor complexes I: Hyperbolicity |
| topic | Group Theory 20F65 (primary) 57M07 (secondary) |
| url | https://arxiv.org/abs/1407.3508 |