Discrete group actions on 3-manifolds and embeddable Cayley complexes
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912217955303424 |
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| author | Georgakopoulos, Agelos Kontogeorgiou, George |
| author_facet | Georgakopoulos, Agelos Kontogeorgiou, George |
| contents | We prove that a group $Γ$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $Γ$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following four 3-manifolds: (i) $\mathbb{S}^3$, (ii) $\mathbb{R}^3$, (iii) $\mathbb{S}^2 \times \mathbb{R}$, (iv) the complement of a tame Cantor set in $\mathbb{S}^3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_09918 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Discrete group actions on 3-manifolds and embeddable Cayley complexes Georgakopoulos, Agelos Kontogeorgiou, George Geometric Topology Combinatorics 57M60, 57S25, 57S30, 57S17, 57K30, 05E45 We prove that a group $Γ$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $Γ$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following four 3-manifolds: (i) $\mathbb{S}^3$, (ii) $\mathbb{R}^3$, (iii) $\mathbb{S}^2 \times \mathbb{R}$, (iv) the complement of a tame Cantor set in $\mathbb{S}^3$. |
| title | Discrete group actions on 3-manifolds and embeddable Cayley complexes |
| topic | Geometric Topology Combinatorics 57M60, 57S25, 57S30, 57S17, 57K30, 05E45 |
| url | https://arxiv.org/abs/2208.09918 |