An endomorphism on immersed curves in the pillowcase
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929421936492544 |
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| author | Herald, Christopher M. Kirk, Paul |
| author_facet | Herald, Christopher M. Kirk, Paul |
| contents | We examine the holonomy-perturbed traceless SU(2) character variety of the trivial four-stranded tangle {p_1,p_2,p_3,p_4} X [0,1] in S^2 X [0,1] equipped with a strong marking, either an earring or a bypass. Viewing these marked tangles as endomorphisms in the cobordism category from the four-punctured sphere to itself, we identify the images of these endomorphisms in the Weinstein symplectic partial category under the partially defined holonomy-perturbed traceless character variety functor. We express these endomorphisms on immersed curves in the pillowcase in terms of doubling and figure eight operations and prove they have the same image. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An endomorphism on immersed curves in the pillowcase Herald, Christopher M. Kirk, Paul Geometric Topology Symplectic Geometry 57K18, 57K31, 57R58, Secondary 81T13 We examine the holonomy-perturbed traceless SU(2) character variety of the trivial four-stranded tangle {p_1,p_2,p_3,p_4} X [0,1] in S^2 X [0,1] equipped with a strong marking, either an earring or a bypass. Viewing these marked tangles as endomorphisms in the cobordism category from the four-punctured sphere to itself, we identify the images of these endomorphisms in the Weinstein symplectic partial category under the partially defined holonomy-perturbed traceless character variety functor. We express these endomorphisms on immersed curves in the pillowcase in terms of doubling and figure eight operations and prove they have the same image. |
| title | An endomorphism on immersed curves in the pillowcase |
| topic | Geometric Topology Symplectic Geometry 57K18, 57K31, 57R58, Secondary 81T13 |
| url | https://arxiv.org/abs/2407.11247 |