Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.08573 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908574740905984 |
|---|---|
| author | Mellor, Blake Wilson, Robin |
| author_facet | Mellor, Blake Wilson, Robin |
| contents | The {\em topological symmetry group} of an embedding $Γ$ of an abstract graph $γ$ in $S^3$ is the group of automorphisms of $γ$ which can be realized by homeomorphisms of the pair $(S^3, Γ)$. These groups are motivated by questions about the symmetries of molecules in space. In this paper, we find all the groups which can be realized as topological symmetry groups for each of the graphs in the Heawood family. This is an important collection of spatial graphs, containing the only intrinsically knotted graphs with 21 or fewer edges. As a consequence, we discover that the graphs in this family are all intrinsically chiral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological Symmetries of the Heawood family Mellor, Blake Wilson, Robin Geometric Topology 57M15 The {\em topological symmetry group} of an embedding $Γ$ of an abstract graph $γ$ in $S^3$ is the group of automorphisms of $γ$ which can be realized by homeomorphisms of the pair $(S^3, Γ)$. These groups are motivated by questions about the symmetries of molecules in space. In this paper, we find all the groups which can be realized as topological symmetry groups for each of the graphs in the Heawood family. This is an important collection of spatial graphs, containing the only intrinsically knotted graphs with 21 or fewer edges. As a consequence, we discover that the graphs in this family are all intrinsically chiral. |
| title | Topological Symmetries of the Heawood family |
| topic | Geometric Topology 57M15 |
| url | https://arxiv.org/abs/2311.08573 |