Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910030860648448 |
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| author | Seo, Donggyun |
| author_facet | Seo, Donggyun |
| contents | We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a right-angled Artin group. The proof proceeds by analyzing the geometry of spheres, tori, and simple closed curves in a doubled handlebody. Along the way, we establish the bigon--bihedron criterion and an equivalent condition for commuting Dehn twists. Furthermore, we construct a compact topological space on which every Dehn twist acts parabolically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group Seo, Donggyun Group Theory Geometric Topology We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a right-angled Artin group. The proof proceeds by analyzing the geometry of spheres, tori, and simple closed curves in a doubled handlebody. Along the way, we establish the bigon--bihedron criterion and an equivalent condition for commuting Dehn twists. Furthermore, we construct a compact topological space on which every Dehn twist acts parabolically. |
| title | Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2511.15063 |