Order-Preserving outer automorphisms of free and surface groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918462337581056 |
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| author | Johnson, Jonathan Le, Khanh |
| author_facet | Johnson, Jonathan Le, Khanh |
| contents | We give a complete classification to when a finite group of outer automorphisms preserves a bi-order on a non-abelian free group and bi-orderable surface groups. We also give another new criterion for an outer automorphism of $F_n$ induced by action of an $n$-strand braid to preserve a bi-order on $F_n.$ Using the new criterion, we produce examples of order-preserving whose underlying permutation is a full cycle which answers in affirmative a question of Kin and Rolfsen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Order-Preserving outer automorphisms of free and surface groups Johnson, Jonathan Le, Khanh Group Theory Commutative Algebra Rings and Algebras 20F60, 20F28 We give a complete classification to when a finite group of outer automorphisms preserves a bi-order on a non-abelian free group and bi-orderable surface groups. We also give another new criterion for an outer automorphism of $F_n$ induced by action of an $n$-strand braid to preserve a bi-order on $F_n.$ Using the new criterion, we produce examples of order-preserving whose underlying permutation is a full cycle which answers in affirmative a question of Kin and Rolfsen. |
| title | Order-Preserving outer automorphisms of free and surface groups |
| topic | Group Theory Commutative Algebra Rings and Algebras 20F60, 20F28 |
| url | https://arxiv.org/abs/2501.18847 |