Topological Symmetry Groups of the Generalized Petersen Graphs
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914266663092224 |
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| author | Álvarez, A. Flapan, E. Hunnell, M. Hutchens, J. Lawrence, E. Lewis, P. Price, C. Vanderpool, R. |
| author_facet | Álvarez, A. Flapan, E. Hunnell, M. Hutchens, J. Lawrence, E. Lewis, P. Price, C. Vanderpool, R. |
| contents | The topological symmetry group $\mathrm{TSG}(Γ)$ of an embedding $Γ$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,Γ)$. If we restrict to orientation preserving homeomorphisms then we obtain the orientation preserving topological symmetry group $\mathrm{TSG}_+(Γ)$. In this paper we determine all groups that can be $\mathrm{TSG}(Γ)$ or $\mathrm{TSG}_+(Γ)$ for some embedding $Γ$ of a generalized Petersen graph other than the exceptional graphs $P(12,5)$ and $P(24, 5)$ (which will be addressed in a separate paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Symmetry Groups of the Generalized Petersen Graphs Álvarez, A. Flapan, E. Hunnell, M. Hutchens, J. Lawrence, E. Lewis, P. Price, C. Vanderpool, R. Geometric Topology 57M15 (primary), 57M50 (secondary) The topological symmetry group $\mathrm{TSG}(Γ)$ of an embedding $Γ$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,Γ)$. If we restrict to orientation preserving homeomorphisms then we obtain the orientation preserving topological symmetry group $\mathrm{TSG}_+(Γ)$. In this paper we determine all groups that can be $\mathrm{TSG}(Γ)$ or $\mathrm{TSG}_+(Γ)$ for some embedding $Γ$ of a generalized Petersen graph other than the exceptional graphs $P(12,5)$ and $P(24, 5)$ (which will be addressed in a separate paper. |
| title | Topological Symmetry Groups of the Generalized Petersen Graphs |
| topic | Geometric Topology 57M15 (primary), 57M50 (secondary) |
| url | https://arxiv.org/abs/2402.08820 |