Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces
We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian immersion. A key ingredient in our proof is the use of compo...
| Main Authors: | , , |
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| Format: | Conference item |
| Language: | English |
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Mathematical Sciences Publishers
2022
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| _version_ | 1797108859123269632 |
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| author | Cazassus, G Herald, C Kirk, P |
| author_facet | Cazassus, G Herald, C Kirk, P |
| author_sort | Cazassus, G |
| collection | OXFORD |
| description | We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian immersion. A key ingredient in our proof is the use of composition in the Weinstein category, combined with the fact that SU(2) holonomy perturbations in a cylinder induce Hamiltonian isotopies. In addition, we show that (S2,4), the 2-sphere with four marked points, is its own traceless flat SU(2) moduli space. |
| first_indexed | 2024-03-07T07:33:56Z |
| format | Conference item |
| id | oxford-uuid:c762b834-9789-4ab6-a5be-383d81ac5fc3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:33:56Z |
| publishDate | 2022 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:c762b834-9789-4ab6-a5be-383d81ac5fc32023-02-13T09:31:02ZTangles, relative character varieties, and holonomy perturbed traceless flat moduli spacesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c762b834-9789-4ab6-a5be-383d81ac5fc3EnglishSymplectic ElementsMathematical Sciences Publishers2022Cazassus, GHerald, CKirk, PWe prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian immersion. A key ingredient in our proof is the use of composition in the Weinstein category, combined with the fact that SU(2) holonomy perturbations in a cylinder induce Hamiltonian isotopies. In addition, we show that (S2,4), the 2-sphere with four marked points, is its own traceless flat SU(2) moduli space. |
| spellingShingle | Cazassus, G Herald, C Kirk, P Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title | Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title_full | Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title_fullStr | Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title_full_unstemmed | Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title_short | Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces |
| title_sort | tangles relative character varieties and holonomy perturbed traceless flat moduli spaces |
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