Simplicial complexes defined on groups
This study makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group, which are preserved by automorphisms of the group, and in many cases have a relation to familiar graphs on t...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-07-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0171 |
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| _version_ | 1849432671792398336 |
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| author | Cameron Peter J. |
| author_facet | Cameron Peter J. |
| author_sort | Cameron Peter J. |
| collection | DOAJ |
| description | This study makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group, which are preserved by automorphisms of the group, and in many cases have a relation to familiar graphs on the group. The ones which seem to reach deepest into the graph structure are two forms of independence complex, and some results on the class of groups for which these two complexes coincide are given. Other examples are treated more briefly. |
| format | Article |
| id | doaj-art-99841a09331d4b14be3e79a480d8cbdb |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-99841a09331d4b14be3e79a480d8cbdb2025-08-20T03:27:18ZengDe GruyterOpen Mathematics2391-54552025-07-01231659410.1515/math-2025-0171Simplicial complexes defined on groupsCameron Peter J.0School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, United KingdomThis study makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group, which are preserved by automorphisms of the group, and in many cases have a relation to familiar graphs on the group. The ones which seem to reach deepest into the graph structure are two forms of independence complex, and some results on the class of groups for which these two complexes coincide are given. Other examples are treated more briefly.https://doi.org/10.1515/math-2025-0171groupindependent setgraphsimplicial complexpower graph05c2520b25 |
| spellingShingle | Cameron Peter J. Simplicial complexes defined on groups Open Mathematics group independent set graph simplicial complex power graph 05c25 20b25 |
| title | Simplicial complexes defined on groups |
| title_full | Simplicial complexes defined on groups |
| title_fullStr | Simplicial complexes defined on groups |
| title_full_unstemmed | Simplicial complexes defined on groups |
| title_short | Simplicial complexes defined on groups |
| title_sort | simplicial complexes defined on groups |
| topic | group independent set graph simplicial complex power graph 05c25 20b25 |
| url | https://doi.org/10.1515/math-2025-0171 |
| work_keys_str_mv | AT cameronpeterj simplicialcomplexesdefinedongroups |