Automorphisms of the sphere complex of an infinite graph
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916428961021952 |
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| author | Hill, Thomas Kopreski, Michael C. Rechkin, Rebecca Shaji, George Udall, Brian |
| author_facet | Hill, Thomas Kopreski, Michael C. Rechkin, Rebecca Shaji, George Udall, Brian |
| contents | For a locally finite, connected graph $Γ$, let $\operatorname{Map}(Γ)$ denote the group of proper homotopy equivalences of $Γ$ up to proper homotopy. Excluding sporadic cases, we show $\operatorname{Aut}(S(M_Γ)) \cong \operatorname{Map}(Γ)$, where $\mathcal{S}(M_Γ)$ is the sphere complex of the doubled handlebody $M_Γ$ associated to $Γ$. We also construct an exhaustion of $S(M_Γ)$ by finite strongly rigid sets when $Γ$ has finite rank and finitely many rays, and an appropriate generalization otherwise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphisms of the sphere complex of an infinite graph Hill, Thomas Kopreski, Michael C. Rechkin, Rebecca Shaji, George Udall, Brian Geometric Topology Group Theory 57S05, 57M07 For a locally finite, connected graph $Γ$, let $\operatorname{Map}(Γ)$ denote the group of proper homotopy equivalences of $Γ$ up to proper homotopy. Excluding sporadic cases, we show $\operatorname{Aut}(S(M_Γ)) \cong \operatorname{Map}(Γ)$, where $\mathcal{S}(M_Γ)$ is the sphere complex of the doubled handlebody $M_Γ$ associated to $Γ$. We also construct an exhaustion of $S(M_Γ)$ by finite strongly rigid sets when $Γ$ has finite rank and finitely many rays, and an appropriate generalization otherwise. |
| title | Automorphisms of the sphere complex of an infinite graph |
| topic | Geometric Topology Group Theory 57S05, 57M07 |
| url | https://arxiv.org/abs/2410.06531 |