Submanifold projections and hyperbolicity in ${\rm Out}(F_n)$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929292085035008 |
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| author | Hamenstädt, Ursula Hensel, Sebastian |
| author_facet | Hamenstädt, Ursula Hensel, Sebastian |
| contents | The free splitting graph of a free group $F_n$ with $n\geq 2$ generators is a hyperbolic ${\rm Out}(F_n)$-graph which has a geometric realization as a sphere graph in the connected sum of $n$ copies of $S^1\times S^2$. We use this realization to construct submanifold projections of the free splitting graph into the free splitting graphs of proper free factors. This is used to construct for $n\geq 3$ a new hyperbolic ${\rm Out}(F_n)$-graph. If $n=3$, then every exponentially growing element acts on this graph with positive translation length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Submanifold projections and hyperbolicity in ${\rm Out}(F_n)$ Hamenstädt, Ursula Hensel, Sebastian Geometric Topology Group Theory The free splitting graph of a free group $F_n$ with $n\geq 2$ generators is a hyperbolic ${\rm Out}(F_n)$-graph which has a geometric realization as a sphere graph in the connected sum of $n$ copies of $S^1\times S^2$. We use this realization to construct submanifold projections of the free splitting graph into the free splitting graphs of proper free factors. This is used to construct for $n\geq 3$ a new hyperbolic ${\rm Out}(F_n)$-graph. If $n=3$, then every exponentially growing element acts on this graph with positive translation length. |
| title | Submanifold projections and hyperbolicity in ${\rm Out}(F_n)$ |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2403.18698 |