Legendrian loops and cluster modular groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929282329083904 |
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| author | Hughes, James |
| author_facet | Hughes, James |
| contents | This work studies Legendrian loop actions on exact Lagrangian fillings of Legendrian links in $(\R^3, ξ_{\st})$. By identifying the induced action of Legendrian loops as generators of cluster modular groups, we establish the existence of faithful group actions on the exact Lagrangian fillings of several families of Legendrian positive braid closures, including all positive torus links. In addition, we leverage a Nielsen-Thurston-like classification of cluster automorphisms to provide new combinatorial and algebraic tools for proving that a Legendrian loop action has infinite order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Legendrian loops and cluster modular groups Hughes, James Symplectic Geometry 53D10 (Primary) 53D12, 13F60 (Secondary) This work studies Legendrian loop actions on exact Lagrangian fillings of Legendrian links in $(\R^3, ξ_{\st})$. By identifying the induced action of Legendrian loops as generators of cluster modular groups, we establish the existence of faithful group actions on the exact Lagrangian fillings of several families of Legendrian positive braid closures, including all positive torus links. In addition, we leverage a Nielsen-Thurston-like classification of cluster automorphisms to provide new combinatorial and algebraic tools for proving that a Legendrian loop action has infinite order. |
| title | Legendrian loops and cluster modular groups |
| topic | Symplectic Geometry 53D10 (Primary) 53D12, 13F60 (Secondary) |
| url | https://arxiv.org/abs/2403.12951 |